# data[].attributes.attachment_link.description
Unleash your creativity with the world's best virtual manipulatives!

# data[].attributes.attachment_link.readable_text
search

Enriching mathematics for all learners

A free-to-use collection of mathematics activities, lessons and problems designed to nurture curious, resourceful and confident learners of mathematics. Produced by The University of Cambridge.

# data[].attributes.attachment_link.description
The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.

# data[].attributes.attachment_link.description
At youcubed, we inspire, educate and empower teachers of mathematics, transforming the latest research on mathematics learning into accessible and practical forms.

# data[].attributes.headline
Number Sense Routines (Choose your grade level!)

# data[].attributes.subject
Number Sense Routines (Choose your grade level!)

# data[].attributes.attachment_link.description
Resources for teaching STEM to students.

# data[].attributes.attachment_link.title
Lesson Activities | Aiming High Teacher Network

# data[].attributes.attachment_link.description
John plans to get the minimum possible Diamond Razor Mesh fencing material, as a security measure to discourage entry into his dam. He finds out that the rectangular shape drawn around the dam picture can help. The dimensions are given in algebraic form, in metres. Find an expression for the area of this [...]

# data[].attributes.attachment_link.readable_text
Place Value

Place Value represents the value of each digit in a number. It is important to learn and understand a number like 724 is made up of 700, 20 and 4, not, 7, 2 and 4. Understanding place value is a key skill to develop in maths. Place value cards are an incredibly useful tool to support children's developing understanding, and these place value arrow cards help to visually represent the value of the digits within a number. Simply lay these handy arrow cards on top of one another to show the different value of each digit within numbers up to ten million.

How else can I use these Place Value Arrow Cards?

With these printable place value cards, you can support individuals in your class, or support whole class teaching. Displaying these place value arrows can work as a fantastic visual reminder for children, and they could form part of your interactive maths display or working wall. These would also work brilliantly as partitioning cards to illustrate how numbers can be partitioned in standard and non-standard ways.

What is the place value of 6 in 67?

All digits within a number have a value, depending on its place, this is called place value. The place value of a digit can be worked out by the face value of that digit x the value of the place. When looking at the number 67, the value of the 6 is worked out by 6 x 10 = 60.

Other versions?

This resource is available in Standard, Black and White, Groups, A5, A3, Black and White Editable, Decimal, alternate colours, Alternative-Colours and 0 to 9. Suggest a new version of this resource

Languages / Countries
Welsh / Cymraeg

# data[].attributes.attachment_link.description
Place Value represents the value of each digit in a number. It is important to learn and understand a number like 724 is made up of 700, 20 and 4, not, 7, 2 and 4. Understanding place value is a key skill to develop in maths.

# data[].attributes.attachment_link.readable_text
JavaScript seems to be disabled in your browser. For the best experience on our site, be sure to turn on Javascript in your browser.

Rainbow Fraction tiles makes understanding fractions easier. With these color-coded tiles, students manipulate parts of a whole to see how they relate to each other. Visualize fractional concepts with this set of 51 proportional plastic pieces.

Color-coding helps students apply their understanding of concepts to new contexts. Students will begin to make mathematical connections with they see that red always equals 1, yellow equals 1/4 and so on.

Includes:

** Rainbow Fraction(R) tiles - represents 1 whole, 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10 and 1/12.
** Plastic tray
** Teacher's guide
** 2 sheets of stickers.

Grades: 1+

Product Description

Rainbow Fraction tiles makes understanding fractions easier. With these color-coded tiles, students manipulate parts of a whole to see how they relate to each other. Visualize fractional concepts with this set of 51 proportional plastic pieces.

Color-coding helps students apply their understanding of concepts to new contexts. Students will begin to make mathematical connections with they see that red always equals 1, yellow equals 1/4 and so on.

Includes:

** Rainbow Fraction(R) tiles - represents 1 whole, 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10 and 1/12.
** Plastic tray
** Teacher's guide
** 2 sheets of stickers.

Grades: 1+

Safety

You may also like

# data[].attributes.attachment_link.description
JavaScript seems to be disabled in your browser. For the best experience on our site, be sure to turn on Javascript in your browser. Rainbow Fraction tiles makes understanding fractions easier. With these color-coded tiles, students manipulate parts of a whole to see how they relate to each other.

# data[].attributes.attachment_link.description
Here's some puzzling fun for the kids from ancient China! Tangrams, "seven pieces of cleverness", are an ancient Chinese puzzle which is still mind-bending and intriguing today! We've developed some fun printable tangram puzzles which are perfect for kids - they help with logic and thinking skills, dexterity ..

# data[].attributes.attachment_link.readable_text
ClassDojo and Stanford's PERTS Research Center teamed up to create the the first season of The Mojo Show. The five-episode video series (along with a few incredible activities) highlight the power of having a growth mindset, and how any student can learn this skill!

# data[].attributes.attachment_link.description
ClassDojo and Stanford's PERTS Research Center teamed up to create the the first season of The Mojo Show. The five-episode video series (along with a few incredible activities) highlight the power of having a growth mindset, and how any student can learn this skill!

# data[].attributes.attachment_link.provider_name
The Robertson Program for Inquiry-based Teaching in Mathematics and Science

# data[].attributes.attachment_link.title
Lessons & resources from The Robertson Program

# data[].attributes.attachment_link.description
Free research-based lessons and resources for educators. Early Years, Primary, Junior. Curriculum Connections. Printables. University of Toronto.

# 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
Authentic Inquiry Maths - how it plays out in the primary/elementary school context

# data[].attributes.attachment_link.title
Math Standard Distribution Links - Grade 3-5

# data[].attributes.attachment_link.description
Interactive links - all | Math and LA Links for Gr. 3 and 4 | Intermediate Math links | Kidspiration Math templates |

# data[].attributes.attachment_link.readable_text
Learning to count is fun with this range of free educational games for Key Stage 1 children. Start with the simple counting games and progress to numbers up to 100. There are also matching and sequencing numbers activities.

# data[].attributes.attachment_link.description
Free, interactive, learning to count games for 5 to 7 year olds involve numbers from 1 to 100.

# data[].attributes.attachment_link.readable_text
Read on to discover lessons, articles, videos, and more. We update the blog regularly to provide you with valuable and timely resources, so visit us often!

Marilyn Burns, mathsolutions35, video

# data[].attributes.attachment_link.description
Read on to discover lessons, articles, videos, and more. We update the blog regularly to provide you with valuable and timely resources, so visit us often! Marilyn Burns, mathsolutions35, video

# data[].attributes.attachment_link.readable_text
In Place Value Pirates, students must use their place value skills to dispatch of the wretched pirate Sir Francis Place Value and his horrible band of place value pirates! Simply read the prompt that appears at the top of the game and click or touch the pirate with the number that matches the prompt. For example, a prompt might read ""7" in the thousands place. Scan the pirates and dispatch of the one with the number that contains a "7" in the thousands place. The game consists of five rounds; each round more challenging the last. For computer versions, users can earn codes after each round so they never have to start all over again. In addition, the game can be played with or without decimals.

# data[].attributes.attachment_link.description
In Place Value Pirates, students must use their place value skills to dispatch of the wretched pirate Sir Francis Place Value and his horrible band of plac

# data[].attributes.attachment_link.readable_text
Now containing 12 851 FREE resources Last updated: 25 May 2006

Rotations

Grids

Numerals

Parallel Lines

Time

Symmetry

Natural World

Angles

Money

Curves

Percentages

Content ©School Improvement Service, EAST RIDING of YORKSHIRE COUNCIL
County Hall, Beverley, East Riding of Yorkshire. HU17 9BA. Tel: +44(0)1482 887700

# data[].attributes.attachment_link.title
eRiding - Media Library - Photographs - Maths - Objects

# data[].attributes.attachment_link.description
Now containing 12 851 FREE resources Last updated: 25 May 2006 Rotations Grids Numerals Parallel Lines Time Symmetry Natural World Angles Money Curves Percentages Content ©School Improvement Service, EAST RIDING of YORKSHIRE COUNCILCounty Hall, Beverley, East Riding of Yorkshire. HU17 9BA. Tel: +44(0)1482 887700

# data[].attributes.attachment_link.readable_text
Each week we'll upload a brand new puzzle, taken from the extensive library of Mathematic Teaching Journals.

You can view all of our journals if you become a member today, for as little as £25 a year! Membership gives you access to the entire library, dating all the way back to issue 1.

That is a LOT of puzzles AND articles AND research AND MATHS!

Puzzle 26 - Taken from MT206

By ATM

Puzzle 25 - Taken from MT199

By Colin Foster, Robin Stewart & Helen Williams

Puzzle 24 - Taken from MT195
By - Stephen Mack
Puzzle 23 - Taken from MT203
By - David Feiss
Puzzle 22 - Taken from MT197
By - John Harrison
Puzzle 21 - Taken from MT213
By - Alan Parr
Puzzle 20 - Taken from MT209
By - Fran Mosley
Puzzle 19 - Taken from MT195
By - Helen Williams
Puzzle 18 - Taken from MT202
By - Ken Duisenberg

Puzzle 17 - Taken from MT200

Puzzle 16 - Taken from MT204
By - Kevin Stone

Puzzle 15 - Taken from MT205

Puzzle 14 - Taken from MT215

By - Paul Stephenson

Puzzle 13 - Taken from MT214
By - Alan Parr

Puzzle 12 - Taken from MT210
By - Phil Dodd

Puzzle 11 - Taken from MT209
By - Paul Stephenson

Puzzle 10 - Taken from MT210

By - Fran Moseley

Puzzle 9 - Taken from MT217

By - Richard Goodman

Puzzle 8 - Taken from MT207

By - Dheepthi Raghavan

Puzzle 7 - Taken from MT220

By - Jenny Murray

Puzzle 6 - Taken from MT211

By - Phil Dodd

Puzzle 5 - Taken from MT201
By - Phil Dodd

Puzzle 4 - Taken from MT196
By - Derek Ball

Puzzle 3 - Taken from MT199
By - Phil Dodd
Puzzle 2 - Taken from MT198
By - Mike Ollerton
Puzzle 1 - Taken from MT195
By - Stephen Mack

# data[].attributes.attachment_link.description
Each week we'll upload a brand new puzzle, taken from the extensive library of Mathematic Teaching Journals. You can view all of our journals if you become a member today, for as little as £25 a year! Membership gives you access to the entire library, dating all the way back to issue 1.

# data[].attributes.attachment_link.readable_text
This week, a workshop on inquiry maths led me to my own 'aha!' moment, as I finally grasped the difference between growth and fixed mindsets, and how it relates to my students.

But how to lead the students to their own 'aha!' moment, without doing the thinking for them?

​" It is possible to write some numbers as the sum of consecutive numbers. For example, 9 is the sum of 4 and 5.

Can you write the numbers 1 to 25 as the sum of consecutive numbers?"

​Working in their books or on whiteboards, students then set to work on this problem. After an initial period of 'thinking time', they were allowed to discuss their thoughts, ideas and strategies with each other. Myself and the learning support teacher were able to ask them questions to draw out their thinking, but did not give them any extra help with the task.

As they grappled with this, we observed their behaviour, and recorded any statements they made.

I then showed this image on the board. Before they went to play, students were challenged to make a connection between this and the statements they had made about their learning.

A few were able to make a connection, some were able to explain what they thought the cartoon was trying to show, while some, comfortable in their fixed mindsets, wrote 'there is no connection' or 'it doesn't make sense.'

3) After play, we got back together as a group. We revisited two terms from our language lessons - 'antagonist' (an adversary who tries to stop the story) and 'protagonist' (an advocate who wants to continue the story) and I explained that in this lesson I wanted students to reflect on whether they were antagonists or protagonists in their own learning story. '
here on Brainpickings.org ):
I then introduced the terms 'fixed' and 'growth' mindset, sharing the example from Carol Dweck's research (summarised
In another study of hundreds of students, Dweck and her colleagues gave each ten fairly challenging problems from a nonverbal IQ test, then praised the student for his or her performance - most had done pretty well.

But they offered two types of praise, some students were told: "Wow, you got [X many] right. That's a really good score. You must be smart at this," while others: "Wow, you got [X many] right. That's a really good score. You must have worked really hard." In other words, some were praised for ability and others for effort. The findings, at this point, are unsurprising yet jarring:

The ability praise pushed students right into the fixed mindset, and they showed all the signs of it, too: When we gave them a choice, they rejected a challenging new task that they could learn from. They didn't want to do anything that could expose their flaws and call into question their talent.

4) The students then asked if they could sort out the statements again, this time into indicators of fixed and growth mindsets. This prompted some very interesting discussion and ideas as they debated where each statement should go. In contrast, when students were praised for effort, 90 percent of them wanted the challenging new task that they could learn from.'

'I think all the questions should go under growth mindset, because questions never end, so they are open to learning.'

'I think the person who said they felt bad might still have had a growth mindset, if they were still trying to work it out. But if they decided that they were no good and gave up, that's fixed. We need more information.'

5) At the end of the lesson, students discussed how their thinking had changed:

'I used to think it was how good you are, but now I think it's more about how hard you try. Even if you're really good at maths, if you're not open in your thinking then you won't ever really challenge yourself, you'll just keep doing the same stuff because it's easy... because it's safe.'

'At first I thought this was a math lesson to wrap my brain in a heap of hardness. But now I don't think it was about the maths at all, but about what I did when it got difficult.'

'I actually think that smart is kind of a bad word because it's either one or the other, you either are or you're not, and that's not what learning is like. Learning just keeps going and going and you're not always going to get it but that doesn't mean that you're not smart, just that you haven't found the answer yet.'

'Yeah, let's ban the word smart!'

Through resisting my natural instinct to manage and redirect her, I had allowed her to come to this realisation about herself and how she learns on her own. An important lesson for her, but for me, too. A reminder of the importance of learning to let go: to unlearn the habits which undermine student inquiry and ownership of their learning. Reflection

Resisting the impulse to manage and direct, taking a step back, and allowing students time and space to come to understanding on their own is the first step towards facilitating authentic inquiries.

​
'I don't think you either have a fixed mindset or a growth mindset and that's it, that's you. I think it can change. For me, I normally try and I don't give up, but today I gave up straight away because I was feeling upset about something that happened at playtime. This makes me think that your mindset depends on how you are feeling. So if you feel sad and alone you won't want to try and you'll be fixed. But if you are happy then you will have a growth mindset. Well... not definitely but you are more likely to have a growth mindset if you are feeling happy.'
During the lesson, I had observed one student with interest. Normally a risk-taker in her learning, as soon as she was challenged by the task she had said 'this is impossible', written the word 'NO.' in large letters on her whiteboard, and then spent the remainder of the time doodling. At the end of the lesson, she shared:

# data[].attributes.attachment_link.description
This week, a workshop on inquiry maths led me to my own 'aha!' moment, as I finally grasped the difference between growth and fixed mindsets, and how it relates to my students. But how to lead the students to their own 'aha!' moment, without doing the thinking for them?

# data[].attributes.body
@mburnsmath

@InquiryPlay

@AJMagicMessage

@MarkChubb3

@Simon_Gregg

@HumanEd_Au

@profkeithdevlin

@rekenrek101

@nrichmaths

@jnovakowski38

@TracyZager

@gfletchy

@joboaler

@SteveWyborney

@ctfosnot

@BuildMathMinds

# data[].attributes.body
Procedures vs Understanding

# data[].attributes.attachment_link.readable_text
Sharing in an app allows educators to pose problems and investigations for students by using an 8-character code or link. Students can share their thinking with their teachers and classmates. Share codes remain available for continued use for 18 months from the date they are last accessed.
Watch the video to learn how sharing works.

# data[].attributes.attachment_link.description
Sharing in an app allows educators to pose problems and investigations for students by using an 8-character code or link. Students can share their thinking with their teachers and classmates. Share codes remain available for continued use for 18 months from the date they are last accessed.

# data[].attributes.attachment_link.authors[].name
with special thanks to Christopher Danielson and his Which One Doesn’t Belong - A Shapes Book.

# data[].attributes.attachment_link.description
with special thanks to Christopher Danielson and his Which One Doesn’t Belong - A Shapes Book.

# data[].attributes.attachment_link.provider_name
Steve Wyborney\\\'s Blog: I\\\'m on a Learning Mission.

# data[].attributes.attachment_link.readable_text
For my educator friends who have access to Google Slides, but do not have access to PowerPoint, this post is for you. Since Google Slides does not have the animation that makes the Splats become transparent, the Splat! reveal does not work in Slides. Now - with these materials - it will. I've rewritten the first 20 Splat! lessons and the first 20 Fraction Splat! lessons with a different method so they will now include the reveal when using Google Slides.

The content of the lessons is the same as the original lessons.

Visit these links to see the original videos about how to use the and the Fraction Splat! slides.

Quick Note: The file sharing power of Google Drive is impressive and highly useful. However, for the purposes of sharing these resources, I need to use a method that I can personally maintain, update and support - and I've learned that the best way to provide resources from my blog is through the download links and the sign-up forms.

I hope you enjoy these Splats! formatted to work in Google Slides!

Splat Through 10
How many dots are under the Splat?
SPLAT 1.1 - numbers through 10 (Google Slides compatible version)
SPLAT 2.1 - with numbers 12-20 (Google Slides compatible version) SPLAT 2.2 - with numbers 12-20 (Google Slides compatible version) SPLAT 2.3 - with numbers 12-20 (Google Slides compatible version) SPLAT 2.4 - with numbers 12-20 (Google Slides compatible version) SPLAT 2.5 - with numbers 12-20 (Google Slides compatible version) SPLAT 1.2 - numbers through 10 (Google Slides compatible version)SPLAT 3.1 - multiple splats (Google Slides compatible version) SPLAT 3.2 - multiple splats (Google Slides compatible version) SPLAT 3.3 - multiple splats (Google Slides compatible version) SPLAT 3.4 - multiple splats (Google Slides compatible version) SPLAT 3.5 - multiple splats (Google Slides compatible version)
SPLAT 4.1 - instant multiple splats (Google Slides compatible version) SPLAT 4.2 - instant multiple splats (Google Slides compatible version) SPLAT 4.3 - instant multiple splats (Google Slides compatible version) SPLAT 4.4 - instant multiple splats (Google Slides compatible version) SPLAT 4.5 - instant multiple splats (Google Slides compatible version) Note: These lessons use a single splat along with a mixture of unit fractions and whole numbers. In Level 11, you control the Splat! SPLAT 11.1 - fraction splats (Google Slides compatible version) SPLAT 11.2 - fraction splats (Google Slides compatible version) SPLAT 11.3 - fraction splats (Google Slides compatible version) SPLAT 11.4 - fraction splats (Google Slides compatible version) SPLAT 11.5 - fraction splats (Google Slides compatible version) SPLAT 1.3 - numbers through 10 (Google Slides compatible version)Note: These lessons use a single Splat! which appears at the same moment as the whole numbers and fractions. Each question instantly presents missing information. SPLAT 12.1 - Instant Fraction Splats (Google Slides compatible version) SPLAT 12.2 - Instant Fraction Splats (Google Slides compatible version) SPLAT 12.3 - Instant Fraction Splats (Google Slides compatible version) SPLAT 12.4 - Instant Fraction Splats (Google Slides compatible version) SPLAT 12.5 - Instant Fraction Splats (Google Slides compatible version) Multiple Splats! with Fractions Note: These lessons include multiple Splats! and you control the timing of the Splats! The entire screen can be seen, the total can be determined, and then Splat! Remember: Each Splat! that is the same color must be covering the same number. SPLAT 13.1 - Multiple Fraction Splats (Google Slides compatible version) SPLAT 13.2 - Multiple Fraction Splats (Google Slides compatible version) SPLAT 13.3 - Multiple Fraction Splats (Google Slides compatible version) SPLAT 13.4 - Multiple Fraction Splats (Google Slides compatible version) SPLAT 13.5 - Multiple Fraction Splats (Google Slides compatible version)
Note: These lessons use multiple Splats! which appear at the same moment as the whole numbers and fractions. Each question instantly presents missing information. Remember: Each Splat! that is the same color must be covering the same number. SPLAT 14.1 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 14.2 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 14.3 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 14.4 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 14.5 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 1.4 - numbers through 10 (Google Slides compatible version)
SPLAT 1.5 - numbers through 10 (Google Slides compatible version)

Splat Through 20
How many dots are under the Splat?

Multiple Splats
Note: Splats that are the same color must cover the same number.

Instant Multiple Splat
Note: An additional feature of this level is the opportunity to ask, "What could the total be?"

Instant Fraction Splat!

Multiple Instant Splats! with Fractions

After reading this blog post, take a look at THE 12 MOST POPULAR MATH STRATEGIES AND DOWNLOADS ON THIS BLOG.

# data[].attributes.attachment_link.title
Splat! for Google Slides - 40 Lessons - Steve Wyborney's Blog: I'm on a Learning Mission.

# data[].attributes.attachment_link.description
For my educator friends who have access to Google Slides, but do not have access to PowerPoint, this post is for you. Since Google Slides does not have the

# data[].attributes.attachment_link.description
Number Rack facilitates the natural development of children’s number sense. Rows of moveable, colored beads encourage learners to think in groups of fives and tens, helping them to explore and discover a variety of addition and subtraction strategies.

# data[].attributes.attachment_link.readable_text
There are so many different views about and practices in math(s) in the Early Years, including the ideas that it's all around us, it's part of a transdisciplinary programme and it's a natural part of how children play.

While I agree with these views, I think as educators, we have an important role in helping children understand mathematical ideas that are indeed in their play, their lives and their world. Mathematical processes and big ideas should be explored explicitly in authentic contexts. A recent tweet by Dr Helen Williams reminded me that thinking is not always a feature when learning mathematics.

In the recent IB publication, The Early Years in the PYP, the reasons why symbolic exploration and expression is important for early learners are explained: "Numeracy involves the capabilities (knowledge, skills and dispositions) needed to understand and use mathematics concepts in a wide range of contexts. Numeracy is a language that we use to communicate. Young learners are developing their numeracy capabilities every day. Through play, they explore and make sense of the world by finding patterns, manipulating shapes, measuring, sorting, comparing, locating, counting and grouping, estimating, connecting, playing with possibilities, posing problems and solving them."

Although this is my first year teaching Kindergarten, my beliefs and guiding principles from my career stay strong. I value inquiry and conceptual learning so that children develop as curious mathematicians, making sense of complex ideas through engaging and relevant contexts. Halliday's framework of learning, learning about and learning through still resonates with me for any single discipline. It reminds me of the importance of the behaviours, passion and mindset of a person actively engaged in a discipline (learning), alongside the mathematical knowledge, skills and concepts that are targeted (learning about) and how the discipline is truly connected to other disciplines and contexts (learning through). I have written more about Halliday here in the context of language.

In her book, Concept-Based Mathematics, Jennifer Wathall reminds us of the importance of processes in maths. Concepts are drawn from these processes as they provide lenses to move beyond just "doing maths", and understanding the why behind the maths.

This post is a chance to reflect on the mathematics in my Kindergarten class so far this year.

Each morning, the children move their photo to take their own attendance. As a class, we then think about how many children are in school that day and how we know. Various strategies are shared.

There is a morning message each day. The day of the week, the month, the year and the actual date all present opportunities to read different numbers and words, explore patterns, consider what has changed and what has stayed the same and anticipate what is to come the next day.

There is also a maths task that focuses on a big idea as part of the morning routine. We spent several weeks subitising and comparing counting strategies using number dots and we are now focusing on estimation using different objects in the classroom. Part of both of these has been the phrasing "How many...?" This has inspired several different wonderings and interest groups going around school to find out how many steps, teachers and rooms we have.

As children play, there are often mathematical ides being explored. This week, a group of children were building a Lego wall thinking about shape, orientation, space and area as they showed great determination to add a layer without any gaps.

Many of the children love to draw and colour. Introducing different types of paper (triangular, squared and, soon, isometric paper) has inspired children to play with design, pattern and symmetry.

Construction is also another popular choice. Recently, as children were trying to build the tallest structures, they started to compare the heights of things. I added a metre stick to their play which prompted them to see who and what was taller and shorter than 1 metre.

Construction often involves exploration of shape, size, space using different materials such as Magna-Tiles, Kapla and interconnecting sticks.

Some children choose to play with Bee-Bots, exploring direction and distance.

There are games, mazes and puzzles for children to play with too. These often require logic, reasoning and strategic thinking which frame fascinating conversations with the children about process.

Building on the children's interests in Pop Its, we have Pop Its with different numbers and arrangements. This one has the standard 100-square written on and has appealed to many children who, despite struggling with numbers in the 'teens', recognised patterns and popped numbers to 100.

The learning environment is instrumental in supporting and provoking mathematical thinking. We are lucky to have lots of loose parts in the classroom. The open-ended nature of these materials offers infinite possibilities and learning beyond mathematics. Within mathematics, children have sorted buttons, counted beads, designed tube-bracelets with patterns and built water walls with tubes and pipes outside. Recently, several children have been playing with balance scales in the classroom and making comparisons about how heavy objects are.

When forming digits in the air, in salt or on paper, many children struggle with where to start and often reverse the digits. We have numbers on display in the class to serve as a model and reference point for where to start.

There is a spiral staircase that connects the Early Years hallway to the playground. We had the numerals 1-10 at the start of the year and these 5-year olds would often count forwards and backwards as they walked and read the numbers. A couple of weeks ago, we changed the numbers starting from 0 and going to 20, skip counting in 2's. This has generated lots of dialogue and choral counting.

In the classroom, there are models and tools to support mathematical thinking. I often use these with small groups of children to target specific number concepts. These include number lines, 100-squares, 10 frames, Numicon, Rekenreks and games such as bingo. There are also some whole-class maths lessons that focus on very specific mathematical concepts and skills. Explicit instruction, high-level questioning and modelling mathematical language in rich contexts are not the enemies of inquiry-based learning. Jo Boaler's Mindset Mathematics - Grade K - is a wonderful resource for ideas for these focused investigations.

Stories are a daily feature in Kindergarten. Stories might be from picture books, poems, rhymes, songs or videos. So often, the stories are based on numbers, patterns, repetition, measurement concepts or the use of shape and space.

We regularly seek opportunities to experience, extend and apply learning beyond the school's walls. At least once a week, we venture into Paris. Last week, we walked along nearby streets to look at architecture and notice 2D and 3D shapes. Shape hunts like this are examples of low-floor, high-ceiling explorations that allow all children to participate but place no limits on learning. Some of these 5-year olds spotted shapes with 7, 9 and 12-sides and wanted to learn the names of these shapes. Walking back to school, one child asked, "What is the name of a 2-sided shape?" This question was launched back to the class the next day as they were challenged to draw a 2-sided shape. A different day, children tallied the number of different shapes they saw.

We regularly visit a nearby nature trail to play, go on scavenger hunts and do team challenges. Many children count the number of things they find or design shapes using natural materials. En route, children are noticing and reading larger numbers more and more.

Sometimes, children explore different areas based on their interests. A few weeks ago, one group was curious about the local fruit and vegetable shop and the jobs of those who worked there. Observing, they noticed the transactions of buying and selling and the prices of different items. They spontaneously started to compare the prices of different produce, understanding the notation for Euros.

Another group was interested in the Metro and who worked there. One of the workers kindly gave the children a Metro map. The children were fascinated with this network of lines and directions, and how to navigate this symbolic representation of the city they lived in. Some children were inspired to make their own maps back at school.

Our current unit of inquiry is under the transdisciplinary theme of How the world works and focuses on the concept of structures. Last week, we walked to the River Seine to observe bridges. Reflecting on the trip, some children were interested in measurements linked to the bridge we walked across (its height and distance across).

I introduced Google Maps and our inquiry then took on a new angle with symbols to show units of measurement. Some children chose to continue playing with this app and Google Earth to explore place, direction and measurement.
Reflections on your Practice
What mathematical learning opportunities do your young learners have?

What other opportunities might be possible?

How do mathematical processes play a role in the learning and teaching of mathematics?

How might there be more opportunities for children to play and be playful with mathematical ideas?

# data[].attributes.attachment_link.description
There are so many different views about and practices in math(s) in the Early Years, including the ideas that it's all around us, it's part of a transdisciplinary programme and it's a natural part of how children play.

# data[].attributes.attachment_link.readable_text
Is the way we talk about maths killing the joy of the subject? Professor Jo Boaler tells Sarah Montague why we must get over our fears of getting it wrong.

Is our attitude towards maths killing the subject for children? Professor Jo Boaler believes a widespread belief in the existence of a 'maths brain' is ruining pupils' chances of success in the subject.

She tells Sarah Montague that anybody can be good with numbers, but unlike other subjects, we teach the idea that some people are simply good or bad at mathematics.

Having researched the way maths is taught in schools in the UK and in the US, Stanford University professor Jo Boaler says pupils are too often made to think that maths is a long list of rules and procedures to be learned off by heart.

In the programme Sarah Montague discovers why real mathematics is about uncertainty; the study of patterns and creative problem solving. She hears about some of the controversial new methods designed to teach flexibility with numbers, which have some parents confounded by the homework their children are being set.

Presenter: Sarah Montague
Producer: Joel Moors.

# data[].attributes.attachment_link.description
Is the way we talk about maths killing the joy of the subject? Professor Jo Boaler tells Sarah Montague why we must get over our fears of getting it wrong. Is our attitude towards maths killing the subject for children?

# data[].attributes.attachment_link.readable_text
Children are naturally mathematical in their play. They play with mathematics.

Early years' practitioners often struggle to make mathematics relevant and engaging for their young learners. In their play, children are naturally mathematical yet practitioners are often unsure about how to build on this or how this observed play 'fits' in with the mathematics they teach.

This book:
*Empowers early years teachers to see the learning in this play and to remain committed to play based practice
*Outlines recent research on how children best learn mathematics
*Supports early years practitioners to know why preparation works better than planning and why ′thinking space′ matters more than you think

# data[].attributes.attachment_link.description
Children are naturally mathematical in their play. They play with mathematics. Early years' practitioners often struggle to make mathematics relevant and engaging for their young learners. In their play, children are naturally mathematical yet practitioners are often unsure about how to build on this or how this observed play 'fits' in with the mathematics they teach.

# data[].attributes.attachment_link.description
This is an example page. It's different from a blog post because it will stay in one place and will show up in your site navigation (in most themes). Most people start with an About page that introduces them to potential site visitors. It might say something like this: Hi there!

# data[].attributes.body
Key Multiplication Facts

# data[].attributes.attachment_link.title
The Chart Shading Routine:  The Day 4 Routine in The Multiplication Advantage

# data[].attributes.attachment_link.title
Using Board Games to Teach Math to Young Children

# data[].attributes.attachment_link.description
Playing board and card games can improve number sense among children as young as 3—and it’s fun!