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Hybrid Plug in the Numbers Interactive Lesson

On the 28th May 2024, Data Education in Schools and Digital Skills Education welcomed a class of 24 students (P7) from Newcraighill Primary School to the University of Edinburgh for the Interactive Lesson Plug in the Numbers, delivered in a hybrid format for the first time. Six primary classes from the...

British Data Awards Ceremony 2024

The Data Education in Schools team are thrilled to have won the 'Education Initiative of the Year' Award at the British Data Awards last night. Jo Spiller (Programme Director) and Jasmeen Kanwal (Project Officer) attended the awards ceremony in the Great Hall of the Grand Connaught Rooms in Covent Garden,...

Creative AI for Teachers

On Tuesday 30th April, Data Education in Schools and Digital Skills Education were delighted to host a workshop for teachers on the use of Generative AI to create art in the classroom. Craig Steele (DES Digital Skills Consultant and Director at Digital Skills Education) and Daniel Devine (Digital Skills Education)...

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Learning with Data - Data Education in Schools

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Empowering school learners to succeed in a data driven future

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Defining Dyscalculia

Dyscalculia is a learning difference that can cause difficulties with core mathematics. It affects approximately 6-8% of the population. It occurs on a spectrum with some people mildly affected and others more severely. With the right understanding, accommodations and support, people with dyscalculia can achieve success in education, the workplace and in wider society.
People with dyscalculia lack an intuitive grasp of simple number concepts or 'number sense'. They have difficulties estimating the magnitude of numbers, exhibit poor understanding of number relationships, and lack fluency with simple numerical operations. Often if the right answer is achieved or the correct procedure followed, it is done so mechanically, with great effort and without confidence.
Dyscalculia is not a general difficulty with learning, it impacts specific skill areas. Dyscalculia is distinct from mathematical difficulties arising from literacy or other learning difficulties, or maths anxiety but can co-occur with these difficulties. The impact of dyscalculia can change according to the environment (i.e. what a dyscalculic person is being asked to do and under what circumstances).

Language, Recognition and Rights

Some people prefer the wording 'a person with dyscalculia', while others prefer the term 'a dyscalculic person'. When working with individuals it is important to use the terminology that the person is most comfortable with. When communicating with a wider audience the terms may be used interchangeably to reflect the variation of preference that exists.

Dyscalculia is a recognised disability under Irish and EU law (such as under equalities, accessibility and disability legislation). However, many dyscalculic people do not consider themselves 'disabled' and this view should be respected.

What difficulties might be experienced by a student with Dyscalculia?

These students often experience difficulties with basic mathematical or numerical tasks or processes such as adding, subtracting, multiplying or dividing. Students can also experience difficulty knowing which mathematical process should be employed based on context.

Other challenges can include telling the time using an analogue watch or clock, handling money or calculating change.

There is a high incidence of co-diagnosis of dyslexia with dyscalculia. This obviously leads to greater challenges for these students.

Students with dyscalculia will often experience a lack of confidence or low self-esteem as a result of previous experiences with trying to study maths.

What can you do to support these students?

New concepts should be introduced using concrete examples only moving to more abstract concepts after these examples have been thoroughly understood by the student.

Multi-sensory teaching can help students who have difficulty with a particular delivery method e.g. visual or aural.

Present mathematical processes or procedures in a number of ways - often students will grasp a concept if it is approached in an alternative way.

Encourage students to ask questions at all stages if they are having difficulty.

Maths teaching should be structured and cumulative and the use of multi-sensory methods employed.

Simple examples should be used for new concepts and concepts should always be introduced at the concrete level with materials before going to maths problems in number, symbol and word form.

The language used should be transparent and students should be encouraged to put mathematical terms into their own words.

Appropriate aids such as number lines, number squares, and calculators should be available, and students should be taught how to use them.

Computer programmes can be useful to help consolidate learning.

Metacognitive strategies will be particularly useful for problem-solving.

The book 'Teaching Numeracy to Children with Dyslexia' by Pauline Clayton may be useful for further strategies.

Have a plan or strategy, which works in any math word problem situation. When a student is presented with a question that requires mathematical calculation, they may benefit from following the 12 steps provided:

1. Read the problem carefully looking for clues and important information. Write down the clues, underline, or highlight the clues.

2. If necessary, rewrite the problem to help find these clues.

3. Look for clues to determine which math operation is needed to solve the problem, for example, addition, subtraction, etc. Look for keywords like sum, difference, product, perimeter, area, etc. They lead to the operation needed to solve the problem.

4. Look for what is needed to solve the problem, for example: how many will are left, the total will be, everyone gets red, everyone gets one of each, etc.

5. Use variable symbols, such as "X" for missing information.

6. Eliminate all non-essential information by drawing a line through distracting information.

7. Draw sketches, drawings, and models to see the problem.

8. Is the word problem similar to previous work, if so how was it solved?

9. Develop a plan based on the information determined to be important for solving the problem.

10. Carry out the plan using the math operations which were determined would find the answer.

11. Does the answer seem reasonable, if it does then it is probably ok - if not then check the work.

12. Work the problem in reverse or backwards, starting with the answer to see if you wind up with your original problem.

Useful Websites

https://ie.ixl.com/math/ provides Irish curriculum-based support from Junior Infants up to 6th year for Maths and English subjects.

Further information and videos which may be helpful can be accessed at http://www.stevechinn.co.uk/

Free multisensory maths tutorials can be accessed at www.alison.com.

www.helpmykidlearn.ie - provides ideas for parents of children aged 0 - 12 to learn on a number of topics, from numeracy, literacy, and communication skills.

http://www.primarygames.com/math.php and http://www.mathplayground.com/ - maths games for children.

Equatio works on Windows, Mac and Chromebook. It lets the user type, handwrite or dictate equations, formulas and more directly to the computer of Chromebook to create mathematical expressions digitally. With intuitive prediction, it can speed up the accuracy of simple and more complex maths expressions.

Books

"What to do when you can't..." series by Steve Chinn.

"Power of 2" series by David J. Sharp (2001).

"The Trouble with Maths: A Practical Guide to Helping Learners with Numeracy Difficulties" by Steve Chinn (2004).

"The Math Handbook; For students with maths difficulties, Dyscalculia, Dyslexia or ADHD" by Helmy Faber (2017).

Dyslexia and Maths Difficulties

Maths difficulties are common in students with Dyslexia. The areas of maths that students with dyslexia find the most difficult are:

The language of maths: Some students struggles to read and understand the vocabulary in maths questions, and therefore do not know what task they are being asked to do. Many different words can be used to describe the same action, e.g. add, increase, plus, total.

Sequencing: The learning of maths is very sequential, but to successfully complete many maths problems a very strict sequence must be followed. Learning multiplication tables is all about learning a strict sequence of information.

Orientation: Difficulties with orientation and direction can lead to confusion of maths symbols. Some people with dyslexia show weakness in the Coding subtest in the assessment, meaning that they struggle to decode symbols accurately and quickly.

Memory: There are many facts, figures, tables, and formulas which have to be learnt and recalled accurately.

Confidence: A lack of confidence in their own maths ability can worsen the above difficulties.

For more information on strategies for dyslexia and maths you can download our handout below:
Dyslexia and Maths Difficulties (PDF)

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Dyscalculia and Maths Difficulties | Dyslexia Ireland

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Dyscalculia is a learning difference that can cause difficulties with core mathematics. It affects approximately 6-8% of the population. It occurs on a spectrum with some people mildly affected and others more severely. With the right understanding, accommodations and support, people with dyscalculia can achieve success in education, the workplace and in wider society.

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Contact Email 1+ (313) 300-1901 Is it a Learning Disability? Dyscalculia Checklist Learning Disabilities Checklist Expert Diagnosis Learning Disabilities Hub

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Want to learn more? Take the free workshop. All 3rd 4th 5th 6th 7th 8th Alg 1 Geom Alg 2 Stat Calc Water Leak Will service arrive in time?Car Ramp How far did the ca…

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Census Schools Resources - CSO - Central Statistics Office

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The goals of the schools resources are to help our students understand what the census is about, to learn how and why a census takes place and the value of census information to society, our communities and our daily lives.

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Arrow Cards is a tablet-friendly place value teaching tool.

Learning Objectives:
Y1: To count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number.
Y1: When given a number, identify 1 more and 1 less
Y2: To recognise the place value of each digit in a two-digit number (10s, 1s).
Y3: To recognise the place value of each digit in a 3-digit number (100s, 10s, 1s)

beads button - changes the concrete example to an abacus, (press again to hide / reveal).
three squares - changes the concrete example to Deinnes cubes, (press again to hide / reveal).
single arrow card - to hide / reveal the arrow cards.
zero button - to zero everything.
stack of arrow cards - to partition your number.

click on any card - to partition that digit.

Why not try counting whilst the arrow cards are hidden.

Have fun!

HAVING TROUBLE LOADING? Please try this version.

This game is © copyright 2021, J.Barrett, ictgames.com All Rights Reserved.

Made using the and libraries.

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Arrow Cards is a tablet-friendly place value teaching tool. Learning Objectives: Y1: To count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number. Y1: When given a number, identify 1 more and 1 less Y2: To recognise the place value of each digit in a two-digit number (10s, 1s).

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I have always loved using games in the classroom. I think games are a great way to reinforce the skills we're targeting while keeping our kids engaged. It's really a win-win teaching strategy for so many reasons!

Math is one of my favorite subject areas, as far as incorporating games goes, so I thought I would share some of my favorite games with you that use a deck of cards.
If you don't have many cards, I would really recommend going to the Dollar Store/Dollar Tree and stocking up...and by that, I mean I would get at least one deck per child, so you'll have more than enough to make your games a success.

So...here they are. Seven math games using cards that will work well for many grade levels, particularly 3rd - 5th. Just a note, most of the games can be tweaked by difficulty (for example Multiplication War could be Addition War), so hopefully, you can make them work for your particular group of kids.

You'll need one deck of cards per student, with all the face cards taken out. To make the game more challenging, you can also remove the 1's (aces) and 2's as well. Players turn over the top card on their deck and the first person to multiply the numbers shown and say the product out loud (not too loud though) is the winner and keeps both cards. If there is a tie, cards go in the middle and the winner of the next round gets that pile too. 1. Multiplication War

2. 30 More or Less

For this game, kids will need 1 - 2 decks of cards (your choice), with only the kings removed. Aces are 1, Jacks are 11, and Queens are 12. One child is designated as "More than 30" and the other is "Less than 30". Each player gets half of the cards and then players flip over their top card.
Students multiply these cards together and if the product is below 30, the Less Than Thirty child keeps the cards and if it is greater than 30, the More Than Thirty child keeps it. If it is exactly 30, the cards are left in the middle and the next winner keeps those cards as well. Play continues until the cards run out. The player with the most cards wins.

3. Place Value Challenge

Use 1 - 2 decks of cards and take out all of the face cards and the 10's. Aces equal one. Once the cards are shuffled and each child gets half, each child turns over the number of cards that you specify...If you're working with hundreds, use 3...One thousands would be 4 and so on. Players may arrange the cards to make whatever number their little heart desires.
You can tell them that the greatest number wins but what I like to do is to use a "More or Less coin" to determine the winner. These are simply made using a round plastic chip, a checker with a sticker in the middle, or a foam circle. I write more on one side and less on the other with a sharpie. That way no one knows the winner and gives up early.
When both players have their numbers ready, the kids flip the coin to see if the highest or lowest number wins and keeps the cards. The one with the most cards at the end is the winner.

4. Build a Number (Either a Humongous Number or a Smaller Number)

This is a different place value game because it really requires higher level, logical types of thinking. Start by taking the face cards and 10's out of the deck(s). Aces equal one.
Kids can make simple place value mats on scratch paper with a dash for each place value (if you're focusing on ten thousands, you need 5 dashes with a comma between the hundreds and thousands). If you like the game and have time, you might want to just make construction paper place value sets and laminate them.
To play the game, shuffle the cards and divide the deck in half for 2 players. Players turn over one card at a time and place it on a dash on the place value mat. Once it is placed, it can not be removed!!!
Here's where the thinking comes in. If you play the Build a Humongous Number game and get a 9, you would want to put that as close to the beginning of the number as possible and if you get a 2, you would want to put it near the end of the number... The player with the biggest (or littlest, if you're playing that game) number wins.
Teaching decimals? This can easily become a decimal place value game. You can even throw in a few joker card s for zeroes!

5. Fraction Battle

This game's purpose is to compare fractions. Start by shuffling the cards. Leave the face cards and aces in. Aces = 11, Jacks = 12, (no 13's for this) Queens = 14, Kings = 15.
Kids need either scratch paper and a pencil or whiteboards and a marker to do a bit of problem-solving.
Split the deck(s) and each player turns over 2 cards that he/she will use to make a fraction. The smaller number is the numerator and the larger is the denominator.
Kid's compare fractions and the larger fraction wins and keeps the cards (unless you use a more/less coin as explained above). If the fractions are equivalent, the cards are put in the middle and the winner of the next round takes those too.

6. Simple Simon Fractions Race (Simplifying Fractions)

To prepare for this game, take out the aces. Make the Jacks 12, Queens 14, and the Kings 15 (no 13's again). Split the deck and shuffle the cards. Each player flips over the top two cards from his/her pile and makes a fraction with the smaller number on top.
The first player (yes it's a race) to correctly simplify his/her fraction may keep the cards from that round. If there is a tie, cards are put in the middle for the next round's winner. If a player's cards can not be simplified, the other player may keep the cards IF he she simplifies his/her own fraction correctly. If not, cards go back in the center for the next round. The player with the most cards at the end wins.

7. Improper Fraction War

Students will need scratch paper or a whiteboard to work out some of their problems in this game. For this game, Aces are one, Jacks are 12, Queens are 14, and Kings are 15. Besides using playing cards to make math more engaging, I love to use task cards. If you're interested in math task cards for any or ALL standards for the entire year for
Shuffle the deck and split the cards evenly. Players turn over the top 2 cards and make an improper fraction (big number on top). Each player converts that improper fraction to a mixed (or regular) number and the largest number wins (or use the more/less coin again).
Winner keeps the cards and play continues. If there is a tie, the cards go in the middle to be taken by the winner of the next round.

More Math Fun:
3rd grade, 4th grade, and 5th grade, I would love for you to check these out.

For more ideas and strategies focused on Upper elementary, be sure to sign up for The Teacher Next Door's free email newsletter right HERE.

Thanks so much for stopping by!

Connect with me:

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Games are a great way to reinforce learning in the classroom. In this post by The Teacher Next Door, you'll learn about seven math games using playing cards that are free and easy too! These math games are perfect for 3rd - 5th graders and will help them master a number of math concepts.

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Browse through over 60 complete K-12 math units of study chalked full of problem based investigations, 3 act math tasks, visual number talks, consolidation prompts and purposeful practice worksheets to Spark Curiosity & Fuel Sensemaking in every student.

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Real World Math Lessons | 3 Act Math Tasks | Math Worksheets & Practice

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Contextual problem based real world math lessons with rich math tasks, multi-day 3 act math tasks, math practice materials and math worksheets

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This tool allows you to create any geometric shape imaginable. Squares, triangles, rhombi, trapezoids and hexagons can be created, colored, enlarged, shrunk, rotated, reflected, sliced, and glued together.

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Basic fact games and tools found in the Math Fact Fluency book

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Google has announced that Jamboards will become “read-only” on October 1, 2024 and will disappear completely on December 31, 2024 (https://support.google.com/jamboard/answer/14084927?hl=en). While we are disappointed in this news, KCM is dedicated to providing resources t…

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1-minute maths app | White Rose Education

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Find out how our ‘1-minute maths’ app can help to build your children’s number confidence and fluency, in just 1 minute!

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Wild Maths - explore, imagine, experiment, create!

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Wild Maths is a collection of mathematical games, activities and stories, encouraging you to think creatively. We've picked out some of our favourites below - have a go at anything that catches your eye. If you want to explore games, challenges and investigations linked by some shared mathematical areas, click on the Pathways link in the top menu.

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Free, Research-Based Materials for Supporting Family Math.

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Number talks are discussions about a particular problem that has been crafted in such a way that key foundational ideas of mathematics can be evaluated and demonstrated. The teacher acts as a guide, not the master, asking students to clarify their thinking, consider and test strategies, investigate and apply relationships, and learn that making mistakes and taking risks can and does lead to success.

The resources below were from discussions in 2014 and 2015 of Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K-5 by Sherry Parrish.
Introduction to Number Talks Number Talks Books Study Presentation on Number Talks Chapters 1-4 Another Presentation on Number Talks Chapters 1-4 Math Talk Rubric Math Talk Bubbles Math Talk Cards Math Talk Moves Poster

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Number talks are discussions about a particular problem that has been crafted in such a way that key foundational ideas of mathematics can be evaluated and demonstrated. The teacher acts as a guide, not the master, asking students to clarify their thinking, consider and test strategies, investigate and apply relationships, and learn that making mistakes and taking risks can and does lead to success.

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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?

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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!

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Home

CHALLENGING MATH PROBLEMS WORTH SOLVING

DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL

WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS?

HERE'S OUR GROWING COLLECTION

WANT TO SHARE OPEN MIDDLE WITH OTHERS?

CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK

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CHALLENGING MATH PROBLEMS WORTH SOLVING DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL Get Our Favorite Problems Take The Online Workshop WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS? HERE’S OUR GROWING COLLECTION Get Google Slide Versions WANT TO SHARE OPEN MIDDLE WITH OTHERS? CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK Elementary Version

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Buntreoir ar Thascanna atá Dúshlánach go Cognaíoch

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Buntreoir ar Thascanna atá Dúshlánach go Cognaíoch

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Math teacher educator Pam Harris and her cohost Kim Montague answer the question: If not algorithms, then what?Join them for ~15 minutes every Tuesday as they cast their vision for mathematics education and give actionable items to help teachers teach math that is Figure-Out-Able. See www.MathisFigureOutAble.com for more great resources!

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Maths Through Stories: Linking Storybooks to Mathematical Ideas

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Maths Through Stories: Linking Storybooks to Mathematical Ideas

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​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
​

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Strategies to support forward & backward number word sequences

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Strategies to support forward & backward number word sequences

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Where are they now?

fluently say the forwards number word sequence to 20

fluently say the backwards number word sequence from 20

confidently name the number before a given amount within the range of 0-30

confidently name the number after a given amount within the range of 0-30

Where to next?
Students:

identify one- and two-digit numerals

say the forward number word sequence to 100, confidently across the decades

say the backward number word sequence to 100, confidently across the decades

say number word just before a given number word without dropping back to one

say number word just after a given number word without dropping back to one

Outcomes

The following activities provide opportunities for students to demonstrate progress towards the following outcomes. A student:

MA1-1WM describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols

MA1-2WM uses objects, diagrams and technology to explore mathematical problems

MA1-3WM supports conclusions by explaining or demnstrating how answers were obtained

MA1-4NA applies place value, informally, to count, order, read and represent two- and three-digit numbers

How?

Bucket count-on-and-back

Drop a small collection of blocks one by one, into a bucket. Ask the students to count aloud as each block is added to the container. After dropping the blocks, show the students the contents of the bucket. Then hold the bucket above the eye level of the students. Ask the students to state how many blocks would be in the bucket if one more block was added. Repeat the question, changing the number of blocks to be added to two and three blocks. Encourage the students to count-on from the number of blocks already in the bucket to find the total. Ask students to record their thinking on mini whiteboards to enable the teacher to see what the students are thinking.

Variations

Ask the students to pretend there are a nominated number of blocks in the bucket and label the bucket using a post-it note. Drop additional blocks into the bucket. Students count-on to find the total sum of the blocks in the bucket

Start with a nominated amount inside the bucket and count back as each block is removed

Increase the number range, or, count forwards and backwards in composite units e.g. by 2s

The counting game

Students select a target number, for example, 34. The goal is to be the student who says that number. Students can count on by saying the next 1, 2 or 3 number words in the sequence. Students collect a counter if they say the target number. A new target number is chosen and students play again.

E.g. Target number 11

Student A: 1, 2, 3...
Student B: 4, 5...
Student A: 6, 7, 8...
Student B: 9, 10, 11... I won!

Variations

Start from a given number and count back, trying to be the person who says zero Students count within a range, for example, starting at 81 and count down to 50 Vary the amount of number words that can be said other than 1, 2 or 3 number words

Why?

These activities encourage and support fluency in counting sequences. An understanding of, and fluency with, number word sequences support students in developing more sophisticated strategies such as counting-on-and-back.

Hundred chart patterns

Display a large hundred chart and provide students with their own, as well as a pile of counters or whiteboard markers, etc. Discuss any number patterns that can be seen on the hundred chart.

Through discussion and investigations, teachers should draw out patterns such as:

There are ten numbers in each row and ten numbers in each column

There are 10 columns and 10 rows

Alternate columns are all odd numbers

Alternate columns are all even numbers

As you go down the hundred chart, each number increases by ten

As you go up the hundred chart, each number decrease by ten

As you go left to right across the rows, each number goes up by one

As you go right to left across the rows, each number goes down by one

Teaching Point
Teachers should take time to investigate patterns by using rich questioning in discussions to challenge student thinking and support deep learning. Making connections between the patterns on a hundred chart and a vertical hundred number line would be useful in showing students a range of representations. Investigating patterns in a 0-99 chart and comparing them to a 1-100 chart, a 1-120 chart and number line would also be beneficial.

Variations

Cut the hundred chart into strips and make a 1-100 number line. Ask students questions such as: Place a marker (or peg, for example) on 7. "What number is ten more than 7? Do we have to count or can we use our knowledge of the hundred chart to help us work out a solution?"

Cut the hundred charts into puzzle pieces. Have the students use the patterns within the hundred chart to restore the chart

Provide incomplete sections of the hundred chart (see example below). Have the students use the patterns within the hundred chart to complete the section provided

Provide students with a blank 10 by 10 grid to represent a hundred chart and fifteen numbered counters (each displaying a different numeral in the range of one to one hundred). Students place the counters onto the grid in the correct numerical position. Explain choices to a partner who checks by counting

Play the hundreds chart game by using two specially made dice, a counter each and a hundred chart each. Students start off with their counter on 50 and take turns to roll both dice. Students predict what square they will land on, their partner records their prediction. They then move according to the dice they rolled and their partner records their move. The first student to reach 100 wins.

Colour it in

Provide students with 2 different coloured markers, questions, 2 x 0-9-sided dice and a 1-120 chart. One student (student A) rolls the dice to form a 2-digit number. The student reads the number to their partner (student B) who records it on the hundred chart using their marker. Student B asks student A one of the following questions:

What is the number before ___?

What is the number after____?

What is the number that comes 2 before __ ? * What number comes 2 after ___?

What number is 10 before ___?

What number is 10 after ____?

What number is 20 before ____?

What number is 20 after ____?

Students should be encouraged to visualise the hundred chart to help them solve their problem. If student A answers correctly, the corresponding number is coloured in. Student B asks an additional question, marking it on the chart if their partner is correct. Students swap turns after the second question, or, if the first student was incorrect. The student with the most coloured in spaces is the winner.
Teaching Point
It is important to expose students to counting numbers beyond 100. As with teen numbers, the numbers between 100 and 120 are often more difficult for students to read.

Before and after: figurative

Prepare "before and after" charts for each pair of students (see example below) with written numerals in the chart. These numerals should be within an appropriate range for the students. Provide the students with numeral cards to sort and place on the chart in either the "number before" or "number after" spaces to form number sequences.
Teaching Point
To scaffold this activity, use charts where the students have to identify only one number before and one number after the given number.

Variations

Add more cards than needed in order to encourage critical thinking and conversation between students. Ask students to prove how they knew where to place each of the numeral cards

Use a range of cards with number words, numerals and images to place in the "before and after" charts

Ask students to place the numeral card that is two before or two after the given number

Add an additional number to the initial chart, or, set it up to support counting by tens

Number line take-over

Provide students with 2 dice, a mini whiteboard and 2 different coloured markers. Have
the first student roll both dice and form a 2-digit number, drawing an empty number line
and recording their number. The second student rolls the dice and forms a 2-digit number, recording it on the same number line. Students continue taking turns to roll the dice and record a number on the number line, aiming to have the most numbers written in order on the number line uninterrupted by their partner's. For example:

Bingo: The number before or after - figurative

Construct bingo cards for each student (BLM - Bingo). The teacher or students write numbers between 1 - 100 on their bingo card. Hold up a numeral card so that all students can see it (or flash a numeral using the interactive whiteboard). Have students check their bingo card, and if it contains a numeral which is one before the numeral displayed, tell them to cover the numeral with a counter. The winner is the first student to cover all of the numerals on his or her bingo card.

Variations

Say the number words and have students identify the numeral before or after

Extend the range of numbers

Instead of numeral cards, show students numerals represented as MAB pictures on cards, concealed numbers on a hundred chart, or ask for the number before, after, two before, two after, etc

Bundling

For students who are learning to count in composite units (groups of 10, for example), present the students with large collections of popsticks. Have the students bundle the popsticks into groups of ten and place any remaining popsticks to the right of the bundles. Students should label the groups of ten as "one group of 10". Encourage the students to count by tens to find the total and add on any remaining popsticks. Students should then label the collection using numeral cards. Interlocking blocks, such as Multi-link, Unifix or Centicubes, could also be used.

This could be used to explore counting by tens forwards and backwards. To support students, provide a template such as the one used in Fences (see emergent section). Students should make piles of 10 pop sticks to form 1 ten. Have the students match the numerals written on the baseboard (10, 20, 30, 40, etc.) as students sequence the pop sticks along the fence.

Zap: figurative

Arrange the students so that they are standing in a circle. Instruct them to count backwards from one hundred down to 83 (for example). Have each student call out one number in the sequence. When the target number (in this case, 83) is reached, the student calls out "zap!" and the person next in the sequence sits down. Continue the activity with the students commencing the backward count again. This process continues until one student remains standing.

Variations

The students count in a forward number word sequence within a given range

Students who are out remain in the circle and continue to say "zapped" whenever it is their turn. The following student continues the count from the number after the number that would have been said instead of "zapped"

Have students record the number words spoken on mini whiteboards once they have been zapped

Count backwards by 10s from 100

Count forwards by 10s to 100

Why?

Students need to know the correct forward and backward number word sequences in order to state the number before or after a given number. Fluency in understanding and recalling the forward and backward sequences is necessary for students to eventually progress to counting-on-and-back.

Using calculators to count

Provide the students with at least one calculator for each pair of students.

Instruct students to:

Enter a given number on the calculator

Use the constant function on a calculator to add on or back from a given number, by ones or by tens

Provide the students with a hundred chart on which they can record the number patterns.

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Activities to support forward and backward number word sequences

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Where are they now? fluently say the forwards number word sequence to 20 fluently say the backwards number word sequence from 20 confidently name the number before a given amount within the range of 0-30 confidently name the number after a given amount within the range of 0-30 Where to next?

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Seo Linn: Leabhrán Ullmhúcháin i gcomhair Teagaisc agus Foghlama

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Seo Linn: Leabhrán Ullmhúcháin i gcomhair Teagaisc agus Foghlama

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Ullmhúchán don Teagasc agus don Foghlaim

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Ullmhúchán don Teagasc agus don Foghlaim

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FIRST® LEGO® League Explore Digital Resources

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FIRST® LEGO® League Explore Digital Resources

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Section A of the DCU - Teacher Guide for Ireland provides the context for FIRST LEGO League Explore.

Within this section you will find the learning principles behind the Explore programme, connections with the Irish Primary Curriculum, the Digital Learning Framework, School Self-Evaluation and the Draft Primary Curriculum Framework.

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Explore Digital Resources to accompany DCU Explore Teacher Guide for Ireland

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Many engineering challenges can be completed using low-cost materials like common craft supplies and recyclables - like cereal boxes and toilet paper tubes. However, students can often struggle to assemble the pieces. They might spend so much time trying to attach wheels that they don't have time to build the car they had planned. As a result, a team of Tufts CEEO students put together a student-facing Constructopedia with building instructions for common mechanisms - like pulleys, hinges, and wheels - from common craft materials and recyclables. Version 2.0 is now available by filling out the form below. You can download the PDF or get a link to the Google Slides, which include animated GIFs.

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Many engineering challenges can be completed using low-cost materials like common craft supplies and recyclables - like cereal boxes and toilet paper tubes. However, students can often struggle to assemble the pieces. They might spend so much time trying to attach wheels that they don't have time to build the car they had planned.

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Article by Jennifer Piggott and Liz Woodham

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This article is based on some of the ideas that emerged during the production of a book which takes visualising as its focus. We began to identify problems which helped us to take a structured view of the purposes and skills of visualising.

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Virtual manipulatives, dynamic geometry, graph plotting, data science and more: explore the ultimate mathematical playground!

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Use this applet to create patterns to cover the screen using regular polygons.

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This requires the ability to attend to the shape and placement of parts when visualising, drawing and modelling 2D and 3D shapes and an understanding of maps and plans, including the words and symbols used on them. It requires a sound understanding of the conventional words and symbols we use to talk about shapes and an understanding of the way in which we classify them using conventional geometric criteria. This also includes an understanding of how patterns and arrangements can be created through the systematic movements (or transformations) of shapes. Thus learning experiences should be provided that will enable students to represent locations, represent shapes, represent transformations and to reason geometrically.

As a result of their learning experiences, students should be able to achieve the following outcomes:

Represent Spatial Ideas

Visualise, draw and model shapes, locations and arrangements and predict and show the effect of transformations on them.

There are three parts to this outcome-Part A: Represent Location, Part B: Represent Shape, and Part C: Represent Transformation. Each is dealt with in a separate chapter.

Reason Geometrically

Reason about shapes, transformations and arrangements to solve problems and justify solutions

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This requires the ability to attend to the shape and placement of parts when visualising, drawing and modelling 2D and 3D shapes and an understanding of maps and plans, including the words and symbols used on them.

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Transformation Game for Kids

Check out this excellent transformation game for kids. Learn about reflection, rotation and translation by completing a number of fun, interactive activities.

Reflect the house onto its shadow by selecting a mirror line and placing it at the correct grid position. When you've completed this, try rotating the house clockwise or anti-clockwise at a certain angle so it covers the shadow again. Complete the translation activity, try more challenges and have fun learning about math with all our free games & online activities.

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Transformation Game for Kids - Reflection & Rotation - Math Games & Activities

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Transformation Game for Kids Check out this excellent transformation game for kids. Learn about reflection, rotation and translation by completing a number of fun, interactive activities. Reflect the house onto its shadow by selecting a mirror line and placing it at the correct grid position.

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INSTRUCTIONS

Use the red buttons to the right to transform the falling blocks.

Completely fill a horizontal row with squares and earn 400 points. Those squares will then disappear, the blocks above will drop into the space leaving more room to complete more horizontal rows.

The game will end when there is no longer room for a block to drop in from the top of the screen.

You can also use the arrow keys on your computer keyboard.

Translate Left Translate Right Rotate 90 degrees Rotate − 90 degrees Rotate 180 degrees Drop

Suggested

Remainder Race

A game involving chance and choice requiring an ability to calculate the remainder when a two digit number is divided by a single digit number.

The short web address is:

Transum.org/go/?to=remainder

Transformation Tetris

Develop your skills translating and rotating shapes in this fast paced classic game.

Tetris is a classic tile-matching game created by a Russian software engineer in 1984.

It has been reported that moderate play of Tetris boosts general cognitive functions such as 'critical thinking, reasoning, language and processing' and increases cerebral cortex thickness.

Rotations and translations are just two of the types of transformations you will learn about on the Maths GCSE course. You can learn more about this topic by doing the online exercise called Transformations.

In addition you will find links to Lesson Starters, curriculum statements, activities, investigations and videos on the main Transformations Topic Page.

The code for Tetris was made available by aerolab, based on code by Peter Coles.

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Develop your skills translating and rotating shapes in this fast paced classic game.

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Regular tessellations use identical regular polygons to fill the plane. The polygons must line up vertex to vertex, edge to edge, leaving no gaps.

Can you convince yourself that there are only three regular tessellations?

Semi-regular tessellations (or Archimedean tessellations) have two properties:

They are formed by two or more types of regular polygon, each with the same side length

Each vertex has the same pattern of polygons around it.

Explore semi-regular tessellations using the Tessellation Interactivity below.
If you've never used the interactivity before, there are some instructions and a video.

The picture shows an arrangement of equilateral triangles and squares. It looks like there's room for another triangle to fill the gap at the top... but can you prove it will fit?

If we tiled the plane with this pattern, we can represent the tiling as {3, 4, 3, 3, 4}, because round every point, the pattern "triangle, square, triangle, triangle, square" is followed. What would the pattern look like if you changed this order?

Can you find all the semi-regular tessellations?

Can you show that you have found them all?

To help you when you are working away from the computer, click below for multiple copies of the different polygons. You can print them, cut them out and use them to test which polygons fit together: 3 4 5 6 8 9 10 12

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md angles polygons and geom proof - stage 3

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Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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'Why tessellation?' you may well be asking. Let me explain. So often in the classroom we try to make activities more enjoyable for the children by varying our teaching to include a more tactile or "hands on" approach. For many, this is their preferred method of learning and, in general, it engages pupils more effectively. There is so much scope for practical exploration of tessellations both in and out of the classroom. It seems a golden opportunity to link art with maths, allowing the creative side of your children to take over. And of course, there is so much maths involved!

Tessellation is a system of shapes which are fitted together to cover a plane, without any gaps or overlapping. The word tessellation itself derives from the Greek tessera, which is associated with four, square and tile. Presumably this is an indication of the fact that tiles of this shape are the easiest to interlock. Tessellations are a common feature of decorative art and occur in the natural world all around us. Two people have principally been responsible for investigating and developing tessellations: Roger Penrose, an eminent mathematician, and the artist, M.C.Escher.

Traditionally, the pattern formed by a tessellation is repetitive. The image that we are likely to think of is known as a regular tessellation , where all the shapes are regular and of the same type, for example:

A semi-regular tessellation is made up of two different regular shapes and each vertex (i.e. point where they meet) is identical. Octagons and squares can be arranged to form a semi-regular pattern:

Roger Penrose took these a step further.

While studying for his PhD at Cambridge, Penrose became fascinated by the geometry of covering a plane. He began by investigating combinations of shapes which would produce a repeating unit, but this led on to a search for a pattern with no repetition. This kind of tessellation became known as quasi-periodic, in other words at first glance there appears to be a repeating pattern, but in fact there is not.

Using only pencil and paper, Penrose found such an arrangement but it contained many different shapes. Amazingly, he managed to reduce this to only six, then just two. The two shapes are both parallelograms and the tessellation is often referred to as "Kites and Darts" :

Although there are small repeated sections, there is no single unit which can be copied to fill the plane. This in itself makes a lovely investigation for children.

Another remarkable man who contributed enormously to the study of tessellation was the Dutch artist M.C.Escher. Born in 1898, initially he concentrated on sketching scenery and surrounding objects. However, on a visit to Alhambra in Spain, he became fascinated by the Arabic tessellating patterns contained in the tiles, and started to experiment more with shapes and mirror images.

Gradually, Escher's work began to change. Rather than drawing what he saw, Escher started to express ideas he had in his mind, creating spatial illusions and detailed repeating patterns. In 1936, Escher made a second trip to Alhambra. Subsequently, his pictures contained more shapes, which were often transformed by reflections, rotations and translations. This produced amazing tessellations of varying complexity:

This tessellation consists of interlocking rectangles which contain the fish and boat images. The rectangles are translated diagonally to produce the entire image. This is one of the simplest types of tessellation.

This second tessellation is much more complicated. It contains interlocking rhombi which have undergone several transformations including translations, rotations and reflection.

All M.C. Escher works (c) 2001 Cordon Art - Baarn - Holland. All rights reserved. Used by permission.

Escher gained a great deal of respect from mathematicians for his work and lectured on art, maths and science.

It is interesting to note that Escher was inspired by the Alhambra Palace in Spain, one of the finest examples of Islamic architecture. Due to the fact that Islamic people were forbidden to represent humans and living creatures in any decorative form, they became masters of tiling patterns and tessellations.

Closer to home, the Great Court of the British Museum in London is another magnificent example of architectural tessellation. Or is it?

Its incredible roof is entirely made up of triangular shaped panes of glass supported by a steel framework. However, although the panes have been fitted together without overlapping or gaps, this is not a true tessellation.

In order to create the curved 3-dimensional roof, the pieces of glass cannot be identical.

Perhaps we could call this a 3-D tessellation?

(c) Copyright The British Museum

Tessellations lend themselves very well to exploration with children. Look around your classroom and school for examples. When a surface is covered tessellating designs are often used. Go out into the playground and perhaps lead into discussion of natural and unnatural tessellations. Our "3-D tessellations" can frequently be found in nature. What about scales on a fish or a tortoise shell? A pineapple's "skin", ears of corn and honeycomb could all be classed as tessellations in 3 dimensions. Challenge the children to find more examples.

Back in the classroom, you can further their understanding of tessellation and develop the mathematical ideas. Using plastic shapes which can be clicked together, allows children to construct the tessellations themselves and this can be easily extended into a 3-D investigation.

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This article describes the scope for practical exploration of tessellations both in and out of the classroom. It seems a golden opportunity to link art with maths, allowing the creative side of your children to take over.

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This tessellation lesson is easy and foolproof.

This particular tessellation tutorial is also a landmark: our first tessellation lesson sent to us by a guest artist, years ago. It came to us from 15-year-old Guest Artist Rachael G*. We salute Rachael's effort and desire to help others.

You can also see this tessellation lesson adapted for Microsoft Windows' "Paint" program and any digital painting program.

Art and Math teacher Jan Miller has this to add, based on using Rachael's tutorial in her classroom:

"The tessellation method from your site which I tried to use with my 3 rd graders was Rachel's 'Papercut Method' but I had a lot of trouble getting it to work. I finally added some little refinements which make it work nearly every time. Step #1 and #3 are to get the tessera to tessellate. Step #2 is to help kids cut accurately. Here are those modifications:

1. Before cutting out the drawn lines we write NW in the northwest corner, SW in the southwest corner, NE in the northeast corner and SE in the southeast corner.

Note from the webmaster: It may make more sense to you if you label the outside corners PART. In step 3, rearrange the PARTs with the letters at the CENTER, so they spell TRAP.
Here are some other word combinations that work: PETS/STEP, POTS/STOP, EVIL/LIVE or FLOG/GOLF, BRAG/GARB or TRAM/MART, TIME/EMIT, PANS/SNAP, or RATS/STAR.

2. Start cutting either line and cut to just past the point where it intersects the other line and stop. Then cut out the entire second line. Now when the kids go back to finish the first line (starting exactly where they left off) we know they will get an accurate cut.

3. Lay the pieces out on the table just as they were before cutting, except leave a little gap in between. Now swap the NE with the SW corners and swap the NW and SE pair.

This seems to work nearly every time. The kids really enjoy knowing that someone closer to their own age invented this method."

See how 4th grade art teacher Karen Weber's class made their own tessellations with this lesson. Her class's do-it-yourself tessellation art gallery shows the final tessellation art AND the handmade patterns that the kids made while producing the art.

*UPDATE: July, 2011.
A professional tessellation artist, David Bailey, has pointed out that someone wrote about this method before Rachael was even born. Perhaps Rachael reinvented it, unaware that someone else had thought along the same lines earlier, or perhaps Rachael simply rewrote Bruce Robertson's technique using her own words and artwork. Either way, it's worth noting that in the years since we first posted Rachael's tessellation tutorial, "Papercut Method" has grown to be Tessellation.org's most popular tutorial and one of our most visited pages.

For those of you interested in looking at that earlier make-it-yourself tessellation lesson, you can find it on page 179 in the book "Learn to Draw Step-By-Step" by Bruce Robertson. The book was published in 1986 by Macdonald publishing house. It's 192 pages, a little less than 30cm x 30cm, and weighs about 0.75 kilograms. Its ISBN-10 number is 0356107892, and its ISBN-13 listing is 978-0356107899. As of 2010, the book is out of print but many used copies are available on Amazon.com for about US$2 plus shipping. I'm buying a copy now; I'll see page 179 when it reaches me in a few months' time.

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Make-your-own Tessellation Lesson - Paper cut method

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Make your own Tessellation Lesson for kids: Simple guide to making an original abstract geometric translation/slide/glide tessellations using pencil, eraser, scissors, and paper.

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This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.

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tessellations created of shapes made out of 'units' composed of a number of squares (the 2 triominoes, 5 quadrominoes (or tetrominoes), 12 pentominoes...) can be interesting to complete and then analyse for their various regularities
such as:

symmetries of the resulting pattern

a parallelogram or 'overlay' that shows the background structure of the tessellation

vectors that are used to move the 'units' to create the tessellation

different tessellations of the same triomino

different tessellations of the same pentomino

ways to start a pentomino tessellation

one way to create a tessellation with this pentomino

joining some corresponding corners gives a parallelogram

moving along the lines of the tessellation between the corners of the parallelogram - what do you notice?

textile art by J Bruce Wilcox:

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ideas and resources for mathematics teachers of 10 to 16 year olds

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An Interior Angle is an angle inside a shape

Another example:

Triangles

The Interior Angles of a Triangle add up to 180°

Let's try a triangle:

90° + 60° + 30° = 180°

It works for this triangle

Now tilt a line by 10°:

80° + 70° + 30° = 180°

Quadrilaterals (Squares, etc)

(A Quadrilateral has 4 straight sides)

Let's try a square:

90° + 90° + 90° + 90° = 360°

Now tilt a line by 10°:

80° + 100° + 90° + 90° = 360°

The Interior Angles of a Quadrilateral add up to 360°

Because there are 2 triangles in a square ...

The interior angles in a triangle add up to 180° ...

... and for the square they add up to 360° ...

... because the square can be made from two triangles!

Pentagon

A pentagon has 5 sides, and can be made from three triangles, so you know what ...

... its interior angles add up to 3 × 180° = 540°

And when it is regular (all angles the same), then each angle is 540 ° / 5 = 108 °
(Exercise: make sure each triangle here adds up to 180°, and check that the pentagon's interior angles add up to 540°)
The Interior Angles of a Pentagon add up to 540°

The General Rule

Each time we add a side (triangle to quadrilateral, quadrilateral to pentagon, etc), we add another 180° to the total:

If it is a Regular Polygon (all sides are equal, all angles are equal)

Shape

Sides

Sum of
Interior Angles

Shape

Each Angle

Triangle
3

180 °

60 °

Quadrilateral
4

360 °

90 °

Pentagon
5

540 °

108 °

Hexagon
6

720 °

120 °

Heptagon (or Septagon)

7

900 °

128.57... °

Octagon

8

1080 °

135 °

Nonagon

9

1260 °

140 °

...

...

..

...

...

Any Polygon
n
( n−2) × 180 °

( n−2) × 180 ° / n

So the general rule is:

Sum of Interior Angles = ( n−2) × 180 °

Each Angle (of a Regular Polygon) = ( n−2) × 180 ° / n

Perhaps an example will help:

Example: What about a Regular Decagon (10 sides) ?

And for a Regular Decagon:

Each interior angle = 1440 °/10 = 144°

Note: Interior Angles are sometimes called "Internal Angles"

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An Interior Angle is an angle inside a shape. Example: ...

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Geoboard is a tool for mathematical exploration. Stretch bands around the pegs to form line segments and polygons, and make discoveries about perimeter, area, angles, congruence, fractions, and more.

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In Tom's house there are tiles on the floor. Each tile is twice as long as it is wide so they each look like this:

How do you think they fit together to cover the floor? Use squared paper to help you to draw your pattern.

Can you find any other patterns?

How many different patterns can you find?

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An activity making various patterns with 2 x 1 rectangular tiles.

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Here is a set of axes with one shape drawn in the first quadrant:

What is this shape called? What are the coordinates of the points A, B, C and D which form the corners of the shape?

Translate (or move) the shape 3 squares to the left and 4 squares up. What are its new coordinates?
Compare these with the original coordinates. What do you notice about the numbers?

Start with the shape above again. This time reflect it in the x axis. What are the coordinates of the corners now?

What do you see when you compare these coordinates with the original ones?

Predict what the new coordinates would be after a reflection in the y axis.

Plot these three points on the graph:

Join the points to make a straight line.
This line is called y = -x because at any point on the line the x coordinate is the same as its y coordinate, but negative.
Reflect the starting shape in the line y = -x and give the new coordinates for A, B, C and D.
Look carefully at these new coordinates and then predict what would happen to these points if they were reflected in the line y = -x:

Now take the original shape again and rotate it 90 o anticlockwise about the origin. What do you notice about the new coordinates?
How else could you describe this transformation?

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What are the coordinates of this shape after it has been transformed in the ways described? Compare these with the original coordinates. What do you notice about the numbers?

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Rotational Symmetry

A shape has Rotational Symmetry when it still looks the same after some rotation (of less than one full turn).

How many times it matches as we go once around is called the Order.

Think of propeller blades (like below), it makes it easier.

Examples of Different Rotational Symmetry Order

Try rotational symmetry yourself with Symmetry Artist ... !

Is there Rotational Symmetry of Order 1 ?

Not really! If a shape only matches itself once as we go around (ie it matches itself after one full rotation) there is really no symmetry at all ...

... because the word "Symmetry" comes from syn- together and metron measure, and there can't be "together" if there is just one thing.

Real World Examples

A Dartboard has Rotational Symmetry of Order 10

The US Bronze Star Medal has Order 5

The London Eye has Order ... oops, I lost count!

849, 850, 2137, 2138, 3360, 3361, 3362, 3363, 5033, 5034

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A shape has Rotational Symmetry when it still looks the same after some rotation.

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Virtual manipulatives, dynamic geometry, graph plotting, data science and more: explore the ultimate mathematical playground!

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Virtual manipulatives, dynamic geometry, graph plotting, data science and more: explore the ultimate mathematical playground!

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There are countless different shapes that can be created using the seven Tangram tiles. What can you come up with?

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Welcome to Geometry and Measurement | NZ Maths

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Geometry Information: a page describing the mathematics that underpins the geometry strand.

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Geometry is all about shapes and their properties.

If you like playing with objects, or like drawing, then geometry is for you!

Geometry can be divided into:

Plane Geometry is about flat shapes like lines, circles and triangles ... shapes that can be drawn on a piece of paper

Solid Geometry is about three dimensional objects like cubes, prisms, cylinders and spheres.

Hint: Try drawing some of the shapes and angles as you learn ... it helps.

Point, Line, Plane and Solid

A Point has no dimensions, only position
A Line is one-dimensional
A Plane is two dimensional (2D)
A Solid is three-dimensional (3D)

Why?

Why do we do Geometry? To discover patterns, find areas, volumes, lengths and angles, and better understand the world around us.

Plane Geometry

Plane Geometry is all about shapes on a flat surface (like on an endless piece of paper).

Polygons

A Polygon is a 2-dimensional shape made of straight lines. Triangles and Rectangles are polygons.

Here are some more:

The Circle

Circle Theorems (Advanced Topic)

Symbols

There are many special symbols used in Geometry. Here is a short reference for you:
Geometric Symbols
Congruent and Similar

Angles

Types of Angles

Using Drafting Tools

Transformations and Symmetry

Transformations:

Coordinates

More Advanced Topics in Plane Geometry

Pythagoras

Conic Sections

Circle Theorems
Triangle Centers
Trigonometry

Trigonometry is a special subject of its own, so you might like to visit:

Solid Geometry

Solid Geometry is the geometry of three-dimensional space - the kind of space we live in ...

... let us start with some of the simplest shapes:

Common 3D Shapes
Polyhedra and Non-Polyhedra

There are two main types of solids, "Polyhedra", and "Non-Polyhedra":

Polyhedra (they must have flat faces):

Non-Polyhedra (when any surface is not flat):

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Geometry is all about shapes and their properties. If you like playing with objects, or like drawing, then geometry is for you! Geometry can be divided into: Plane Geometry is about flat shapes like lines, circles and triangles ...

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Sort a variety of 2-D shapes on a Carroll diagram. Sort by one or two conditions. Sort triangles, quadrilaterals, pentagons, hexagons, heptagons and octagons, as well as parallelogram, rhombus, kite and trapezium. Also sort according to a shapes propertie

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Welcome to MathScify Assessment

Access a repository of tasks to assess critical numeracy and scientific skills

Embed formative assessment seamlessly into everyday classroom practice

Monitor student' progress using a variety of assessment frameworks

Inspire learners to make decisions, explain and justify their thinking

Empower learners to create new ideas and represent their thinking in multiple ways

Utilise problem-posing scenarios to foster agency

Enhance all learners' awareness of, progress, and confidence in mathematics and science

Guide next steps in learning through effective feedback

Build a portfolio of student' work

About MathScify Assessment

MathScify Assessment is a research-based initiative that has been developed in line with the principles of universal design for learning.

"Everyone is a genius. But if you judge a fish on its ability to climb a tree, it will live its whole life believing it is stupid "

Our mission is to provide an opportunity for all students to showcase and celebrate their achievements in mathematics and science

Join Our Mission

Stay informed and receive our newsletter and updates, featuring exciting discoveries, research, and advancements in the world of mathematics and science. Empowering Minds through Mathematics and Science

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Mathematics & Science assessment for teachers & their students - Mathscify

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Mathscify is an innovative mathematics and science assessment for teachers and their students to assess essential mathematical and science skills.

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Mata go Deo! - sraith póstaer agus pacáiste tacaíochta - An Gum

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Mindsets & Maths Achievement (Carol Dweck)

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Mindsets & Maths Achievement (Carol Dweck)

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Family maths? What's that? We're on a mission to give all families and communities playful, hands-on, creative experiences of maths that they can do together - we want everyone in the UK to enjoy and feel positive about maths!

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We're on a mission to give all families and communities playful, hands-on, creative experiences of maths - we want everyone to feel positive about maths!

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Maths Anxiety: Hand Model of the Brain (Dr. Daniel Siegel)

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Maths Anxiety: Hand Model of the Brain (Dr. Daniel Siegel)

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Dr Daniel Siegel presenting a Hand Model of the Brain

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Picture Books useful for Maths (NZ Maths)

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Picture Books useful for Maths (NZ Maths)

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Math Modeling: Getting Started & Getting Solutions

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Math Modeling: Getting Started & Getting Solutions

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14 Practices to build Thinking Classrooms

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14 Practices to build Thinking Classrooms

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If we want our students to think, we need to give them something to think about-something that will not only require thinking but also encourage thinking. In mathematics, this comes in the form of a task, and having the right task is important. The research revealed that we have to give thinking tasks .

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Universal Design for Learning  Guidelines

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Universal Design for Learning  Guidelines

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The UDL Guidelines are a tool used in the implementation of Universal Design for Learning, a framework to improve and optimize teaching and learning for all people based on scientific insights into how humans learn. Learn more about the Universal Design for Learning framework from CAST. The UDL Guidelines can be used by educators, curriculum developers, researchers, parents, and anyone else who wants to implement the UDL framework in a learning environment. These guidelines offer a set of concrete suggestions that can be applied to any discipline or domain to ensure that all learners can access and participate in meaningful, challenging learning opportunities.

Reenvisioning the UDL Guidelines

Because the UDL Guidelines are meant to be informed by feedback from the field as well as new research, they have been updated several times in the past. We are in the process of updating the Guidelines once again in our UDL Rising to Equity initiative.

This update will focus specifically on addressing systemic barriers that result in inequitable learning opportunities and outcomes. CAST aims to develop a transparent, inclusive, and community-driven process. If you are interested in collaborating and staying updated on our progress, we invite you to complete a brief survey.

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The UDL Guidelines are a tool used in the implementation of Universal Design for Learning, a framework to improve and optimize teaching and learning for all people based on scientific insights into how humans learn. Learn more about the Universal Design for Learning framework from CAST. The UDL Guidelines can be used by educators, curriculum developers, researchers, parents, and anyone else who wants to implement the UDL framework in a learning environment. These guidelines offer a set of concrete suggestions that can be applied to any discipline or domain to ensure that all learners can access and participate in meaningful, challenging learning opportunities.

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Cruth agus spás: Feasacht ar spásúlacht agus suíomh

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Cruth agus spás: Feasacht ar spásúlacht agus suíomh

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Ailgéabar: Patrúin, rialacha agus coibhneasa

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Ailgéabar: Patrúin, rialacha agus coibhneasa