# data[].attributes.headline
PDST Numeracy Manuals: A Guide for Teachers

# data[].attributes.subject
PDST Numeracy Manuals: A Guide for Teachers

# data[].attributes.attachment_link.title
PDST Numeracy handbooks: A Guide for teachers

# data[].attributes.headline
Manual: PDST Measures P 274 Using Stories

# data[].attributes.subject
Manual: PDST Measures P 274 Using Stories

# data[].attributes.attachment_link.description
Can you spot circles, spirals and other types of curves in these photos?

# data[].attributes.headline
PDST Numeracy Manuals: Please click here to access all manuals

# data[].attributes.subject
PDST Numeracy Manuals: Please click here to access all manuals

# data[].attributes.attachment_link.readable_text
The following teacher handbooks are intended to complement and support the implementation of the Primary School Mathematics Curriculum (PSMC). By providing additional guidance in the teaching and learning of mathematics, the publications attempt to illuminate an instructional framework for enhancing mathematical thinking. This instructional framework advocates methods of eliciting, supporting and extending higher-order mathematics skills such as reasoning; communicating and expressing; integrating and connecting; and applying and problem solving.

​Click on this link for a guide on how to use our manuals guide.

​ ​Just click on the title of each manual to view or download. Print copies of any manual can be ordered from Laois Education Centre here.

# data[].attributes.attachment_link.description
The following teacher handbooks are intended to complement and support the implementation of the Primary School Mathematics Curriculum (PSMC). By providing additional guidance in the teaching and learning of mathematics, the publications attempt to illuminate an instructional framework for enhancing mathematical thinking.

# data[].attributes.headline
Nrich: Story Books to Develop Mathematical Concepts

# data[].attributes.subject
Nrich: Story Books to Develop Mathematical Concepts

# 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.readable_text
Geometric Chalk Designs:

Ask the following mathematical questions when you are admiring your work:

How many sections do we have in total?

How many parts are pink?

What colour is the most common? How many?

Which section has the largest/smallest area?

Which section has the largest perimeter? How can we be sure?

What fraction of the design is green?

What percentage of the design in blue?

What is the fewest number of colours you can use so that no adjacent sections are the same colour? Can you create a design that requires more colours than your original one?

Resource credit: www.youcubed.org

MAZES:

A maze is great fun and it can be a maths learning experience too!

Mazes offer open ended problem solving for all ages in an imaginative and creative environment. They help people develop mathematical logic skills and require participants to memorise lengthy sequences of moves in a particular order.
Jumping Julia
Help Julia get from start to finish. The number on each square indicates how far you can move. You may jump horizontally or vertically, but not diagonally.

Get the students to design the 5 x 5 square grid:

discuss the properties of squares - the four sides of the squares should be of equal length.

Decide on the length of each small numbered square. Then multiply this number by 5 to calculate the length of the overall 5 x 5 grid.

Students should familiarise themselves with the equipment used to measure length - decide on appropriate units to use and measure out the required dimensions.

Resource credit: Julia Robinson Mathematics festival (jrmf.org)

# data[].attributes.attachment_link.description
Maths at Home Activities Here we present daily activities that you can do at home Scroll down for previous activities This page may be slow to load as there is a lot of content. For March, April and May we presented daily Maths at Home activities. You can

# data[].attributes.headline
PDST Resource: Play Based Maths Picture Books

# data[].attributes.subject
PDST Resource: Play Based Maths Picture Books

# data[].attributes.attachment_link.description
MathsThroughStories.org is a non-profit and research-based initiative, based at the University of Reading's Institute of Education (UK). It sets out to help mathematics learners around the world...

# data[].attributes.attachment_link.readable_text
One dot can make a sun or moon when day is done. Two dots can make the eyes of a fox or the eyes of keys that open locks.

Children count all the way to ten with simple rhymes and brightly coloured objects

The activities below extend the learning from this book.

This lovely video looks at simple counting, size and position. Here are some resources to go with it.

Learning to count has never been more fun than in this crazy tale of a dog, a lion and a tiger all showing off how many apples they can balance on their heads as they skip, walk the tightrope and roller skate their way through the book.

Have fun with numbers in this hilarious new picture book by master storyteller and illustrator Tony Ross.
"One hundred shoes, please!" said the little centipede. "Fifty left ones, and fifty right ones."
"Why do you want one hundred?" asked the shoe seller.
"Because I'm a centipede, which means a hundred feet," said the little centipede.
But when are one hundred shoes too many shoes? And what do you do with too many shoes? Why, you give them away!

Find out who gets them in this delightfully silly story about a centipede with sore feet.

A favourite amongst primary school teachers, through Elmer you can teach:

Shape, colour, patterns, size, grouping, multiplying by 2 with the tusks or by 4 with feet.

Resources below:Resources magpied from various sources.

# data[].attributes.attachment_link.description
Welcome to the Maths Story Shed. Stories are a great way to hook children when teaching maths, hopefully these stories will enthuse your children and become a great resource. Don't forget we now have...

# data[].attributes.attachment_link.readable_text
Here are three little cars, each going on a journey.
For this activity, you will need three little cars. We are going to see how far they can travel.
You might use a small wooden ramp, like this:

Or you could make one using materials you have got.
You may like to use a big slide, like this one:

If the ramp is wide enough, place all three cars at the top and LET GO!
Which went furthest? How do you know?
How far did each one travel from the bottom of the slope?
What could you try next?

Photograph Acknowledgement
www.skatebuilders.com
www.tripadvisor.com

# data[].attributes.attachment_link.description
This practical activity involves measuring length/distance.

# data[].attributes.attachment_link.readable_text
This is the start of the $100$ metres in $1896$. In that year Thomas Burke from the USA won the race in $12$ seconds.

I wonder how far you could run in $12$ seconds.

You and your friends could use a stop watch and then measure how far you ran.

This is the finish of the $200$ metres in $1924$. Jackson Scholz from USA won that race in just over $21$ seconds.

I wonder if you could run the $100$ metres in that time?

Or you could see how far you could run in $22$ seconds.

This is the high jump in $1906$. It shows Ray Ewry from the United States.

He jumped $1$ metre $56$ centimetres.

How high can you jump?

See how high $1$ metre $56$ centimetres is.

Can you find someone who can jump that high?

# data[].attributes.attachment_link.description
This is the start of the $100$ metres in $1896$. In that year Thomas Burke from the USA won the race in $12$ seconds. I wonder how far you could run in $12$ seconds. You and your friends could use a stop watch and then measure how far you ran.

# data[].attributes.attachment_link.readable_text
Invite pupils to either find or create a weight of 100g. Next ask the pupils to choose from a variety of substances such as rice, porridge, pasta, peas, etc. Pupils will then estimate how much of each substance they will need to make a 100g weight by filling individual bags/tubs. Pupils will weigh their estimates and can add/remove weight accordingly to reach the 100g target. When all bags weigh 100g consider the following questions:

This activity can be adapted to use different target weights.
PDST Measures Manual p.145 PDST Tomhais Lámhleabhar an Mhúinteora lch.166

# data[].attributes.attachment_link.description
Invite pupils to either find or create a weight of 100g. Next ask the pupils to choose from a variety of substances such as rice, porridge, pasta, peas, etc. Pupils will then estimate how much of each substance they will need to make a 100g weight by filling individual bags/tubs.

# data[].attributes.attachment_link.description
Please note: Activities marked with * were created to support distance learning

# data[].attributes.headline
PDST Measures Manual: Just a Minute p.237

# data[].attributes.subject
PDST Measures Manual: Just a Minute p.237

# data[].attributes.attachment_link.readable_text
Getting Started

1. Begin by brainstorming the words we use to talk about time and listing these. For example, 20 past/to, quarter or half past/to, o'clock, four fifty, hours, minutes and seconds.

2. Explain to the students that there are several different ways to describe time and this week they are going to explore two of these.

3. Show an analogue clock and discuss the face, drawing out the students' experiences with clocks and time.
What can you tell me about the face?
What numbers are there? Why (is there nothing above 12)?
How are the numbers arranged? Why?
Tell me about the clocks that you have at home?
What is the biggest clock you have ever seen?
When do you get up?
When do you go to school?

4. Have each student construct an analogue clock:
Draw around an object to make a circle of light card or give each student a cut circle of card.
Fold the circle in half and colour each half a different colour - this helps reinforce the concept of half.
Make a big and a small hand and attach these with a split pin.
Draw numbers onto the clock-face.

Exploring
Analogue Time

1. As a group, discuss times of the day when well known events happen and have the students model these times on the analogue clocks they have made. At first focus on hours, e.g. school starts at nine o'clock; eight o'clock is bedtime. Then move on to half-hours, e.g. half past ten is playtime.

2. As students work at modelling times, focus on the position of the hands (big hand shows minutes and little hand shows hours) and the terms half past and o'clock.

3. Students can record some of their favourite times of the day and draw clocks showing those times.

Analogue Time Problems
Pose several problems involving time (to hours and half-hours). Place these problems on cards stationed around the room and have the students work with a buddy and their analogue clock to solve them and record their answers. As a group, discuss the problems and their solutions.

Possible problems include:

Sally went swimming at 4 o'clock and got out of the pool at half past five. How long did she swim for?

If it takes half an hour to walk to school from home, how long will it take to walk to school and back home again?

Laura had an appointment at the dentist at half past three. She didn't arrive until 4 o'clock. How late was she?

The movie started at 6 o'clock and finished at half past seven. What was the running time of the movie?

Mark went to bed at 8 o'clock and woke up 11 hours later. What time did he wake up?

Muffins take half an hour to cook. If a batch of muffins goes into the oven at half past five what time will they be ready?

Digital Time

1. Have the students carefully examine a digital clock and count the number of minutes in each hour. Establish that there are 60 minutes in each hour, and therefore 30 minutes in half an hour. This is also a good opportunity to practice skip-counting with fives.

2. Establish with the students that the first number of the digital clock shows the hour and the second number shows the number of minutes past that hour.

3. Challenge the students by asking them how they think the digital clock would show times that they are familiar with on an analogue clock e.g. nine o'clock (start of school), and half past ten (play time).

4. Reinforce the fact that half an hour is thirty minutes, therefore digital times ending in 00 are the same as o'clock and times ending in 30 are the same as half past.

5. List some of the students' favourite TV programmes and have the students record the digital times these programmes come on. Look at a TV guide to confirm the times that they have recorded.

Digital Time Problems

Pose several problems involving time (to hours and half-hours). Place these problems on cards stationed around the room and have the students work with a buddy to solve them and record their answers. As a group, discuss the problems and their solutions.

Possible problems include:

Sally went to play netball at 4.00 and came home at 5.30. How long was she away?

If it takes 30 minutes to walk to the beach from home, how long will it take to walk to the beach and back home again?

Laura had an appointment at the doctor at 2.30. She didn't arrive until 3.00. How late was she?

Hine's TV programme started at 7.00 and finished at 8.30. How long was the programme?

Mark went to his grandma's at 2.00 and stayed there for 6 hours. What time did he leave?

Potatoes take 30 minutes to boil. If Mum wants the potatoes to be ready by 5.30, when must she put them in the boiling water?

Mixed Time

1. Divide the class into two groups. One of these is the analogue group and the other the digital group. Give each group an appropriate clock,

2. Let the analogue group choose a time (involving hours or half-hours). Get the digital group to show that time on their clock.

3. Then let the digital group choose a time and ask the analogue group to show it on their clock. Repeat this a few times.

4. Choose any time. Ask questions like
Show me the time in half an hour?
What will be the time 3 hours from now?
What was the time 30 minutes ago?
What will be the time in 60 minutes?
What was the time three half hours ago?

5. Get the groups to make up their own problems like this and like the ones we used earlier. Allow the students to ask each other the questions. Get the students to draw their answers using drawings of both an analogue clock and a digital clock.

6. Ask the students to tell you the main times of the day (when school starts, play time, lunchtime, etc.). Get them to draw these in both analogue and digital formats. Put a selection of their drawings on the wall to refer to later.

Sharing

Over the course of one day have each student keep a record of what they are doing on the hour and at half past the hour. To help you remember, set a digital alarm clock to go off every half-hour, getting the students to help with this. Have students record what they are doing along with the analogue time in a diary.

Compare the differences and similarities in the students' diaries.

Pose the following questions for discussion during the day.
Why is the term 'half past' used to tell the time?
In the term 'half past', what does the word 'half' refer to?
What are the units of time?
What is the relationship between minutes and hours?

# data[].attributes.attachment_link.description
Getting Started Begin by brainstorming the words we use to talk about time and listing these. For example, 20 past/to, quarter or half past/to, o'clock, four fifty, hours, minutes and seconds. Explain to the students that there are several different ways to describe time and this week they are going to explore two of these.

# data[].attributes.attachment_link.title
How Long Is a Minute? | PBS LearningMedia

# data[].attributes.attachment_link.description
Track how well you can judge how long a minute lasts. This interactive exercise focuses on estimating lengths of time and reading a table. This resource is part of the Math at the Core: Middle School Collection.

# data[].attributes.headline
Virtual Manipulative: The Teaching Clock

# data[].attributes.subject
Virtual Manipulative: The Teaching Clock

# data[].attributes.attachment_link.description
Teaching Clock is an open-ended teaching resource to help primary age children explore telling the time in both analogue and digital formats.

# data[].attributes.attachment_link.readable_text
Do you know those calendars that are a series of cards, one for each month?
I have one of those on my desk at home.

The cat jumped on my desk while I was at school yesterday and knocked it off on to the floor.
Now they are all muddled up.
I do not know which month is which and I don't know how to put them back in the right order.
Can you help?

Here is a sheet you can print off and cut up into twelve cards, one for each month. Or you could use the interactivity below which allows you to drag the month cards so you can try out your ideas.

Can you put the cards in the right order?

# data[].attributes.attachment_link.description
Do you know those calendars that are a series of cards, one for each month? I have one of those on my desk at home. The cat jumped on my desk while I was at school yesterday and knocked it off on to the floor. Now they are all muddled up.

# data[].attributes.attachment_link.title
Interactive Clock | Telling Time | Analog & Digital | Toy Theater

# data[].attributes.attachment_link.description
Use the online teaching clock for a fun digital experience with your students. Students can learn to tell time with both analog and digital clocks!

# data[].attributes.attachment_link.readable_text
Rosie went into the sweet shop with $10$p to spend.

There were chews for $2$p, mini eggs for $3$p, Chocko bars for $5$p and lollypops for $7$p.

What could she buy if she wanted to spend all her money?

Alice, James, Katie and Henry went into the shop too. They each had $20$p to spend and they all spent all of their money.

Alice bought at least one of each kind of sweet. Which one did she have two of?

James spent his money on just one kind of sweet, but he does not like chews. Which sweets did he buy?

Katie bought the same number of sweets as James but she had $3$ different kinds. Which sweets did she buy?

Henry chose $8$ sweets. What could he have bought?

(If you want to do this with cents instead go here )

# data[].attributes.attachment_link.description
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

# data[].attributes.attachment_link.title
Practising Second class maths: ‘Least number of coins’

# data[].attributes.attachment_link.description
Improve your maths skills by practising free problems in ‘Least number of coins’ and thousands of other practice lessons.

# data[].attributes.attachment_link.readable_text
QR CODE

Scan this on mobiles and tablets to quickly open this web page.

Coins game is a money game which introduces children to coinage in British, Australian, American and Euro currencies. The currency defaults to British, but can be changed by clicking on the flags. The game is designed for 4-10 year olds.

It has three game modes. The first activity, Sorting, helps children to recognise the different coins. The second, Ordering, involves arranging the coins from lowest to highest values. Thirdly, the Counting game has eight different ability levels where children count the amounts of money on a piggy bank. It can help to improve children's accuracy in counting money and it is useful for classroom money activities as a better alternative than plastic money. All three activities lend themselves well to use on an interactive whiteboard.

AGE

4-10 Years

SUBJECTS

Maths Money

# data[].attributes.attachment_link.description
Free sorting, ordering and counting games for 4 to 10 year olds. British, Australian, American and Euro currencies supported.

# data[].attributes.attachment_link.description
What do you think is going to happen in this video clip? Are you surprised?

# data[].attributes.headline
PDST Measures Manual: Popcorn Project P.189

# data[].attributes.subject
PDST Measures Manual: Popcorn Project P.189

# data[].attributes.headline
PDST Measures Manual: Nine Layer Density Tower p.192

# data[].attributes.subject
PDST Measures Manual: Nine Layer Density Tower p.192

# data[].attributes.attachment_link.readable_text
With this science-magic trick, you'll put a new spin on our famous Density Column demonstration. First, you'll discover how to stack nine layers of liquids on top of each other. That alone looks really cool, but then you take it up a notch by making different solid objects "float" in the middle of all those cool looking stacked liquids. You'll surprise yourself and your friends with what you can do with the 9-Layer Density Tower.

Experiment Materials

Liquid Materials, 1.5 to 3.5 oz (50 to 100 ml) of each:

Honey

Corn Syrup

100% Maple Syrup

Whole Milk

Dish Soap

Water

Vegetable Oil

Rubbing Alcohol

Lamp Oil

Other Materials:

1 Quart (1L) container - tall, narrow, clear

9, 4 oz (118 ml) plastic cups

Turkey baster

Food coloring

Metal bolt

Popcorn kernel

Board game die

Cherry tomato

Plastic beads

Plastic soda cap

Ping-Pong™ ball

How Does It Work

Density is basically how much "stuff" is packed into a particular volume. It's a comparison between an object's mass and its volume. Remember the all-important equation: density = mass ÷ volume. Based on this equation, if the weight (or mass) of something increases but the volume stays the same, then density goes up. Likewise, if the mass decreases but the volume stays the same, then density goes down. Lighter liquids (like water or vegetable oil) are less dense than heavier liquids (like honey or corn syrup) so they float on top of the heavier liquids. The same amount of two different liquids you used in the container will have different densities because they have different masses. The liquids that weigh more (a higher density) will sink below the liquids that weigh less (a lower density).

To test this, you might want to set up a sensitive kitchen scale and weigh each volume of the liquids that you added to the column. Make sure that you weigh identical volumes of each liquid. You should find that the weights of the liquids correspond to each different layer of liquid. For example, the honey will weigh more than the dish soap. By weighing the same volume (e.g. ¼ cup, 60 ml) of these liquids, you will find that density and weight are closely related.

By convention, plain water has a density of 1.0 and that's measured in g/cm ³ or g/ml. So, a cubic centimeter of water has a mass of 1 gram and fills 1 milliliter of volume. If a substance has a density less than 1.0 g/cm ³, it floats on water and one with a density more than 1.0 g/cm ³, it sinks in water. The numbers below are based on data from manufacturers for each item. Since each manufacturer has its own "secret" formula, densities may vary slightly from brand to brand for the same product but these are pretty close.

The same rule for "sink or float" goes for the small objects that you dropped into your density column. The metal bolt is more dense than all of the liquids in the column and therefore sinks directly to the bottom. Less dense objects will float on individual layers up the column. For instance, the plastic beads are more dense than the vegetable oil and everything above it but less dense than the water and everything below it. This makes the beads settle on top of the water. The Ping-Pong ball is the least dense of it all and floats on top.

Take It Further

This is the perfect opportunity to get in some scientific exploration. Use what you learned from dropping the beads, soda bottle cap, tomato, and game die into the container to figure out which items are more or less dense than water. Which items have more density than vegetable oil? What items are less dense than honey? You could make a hypothesis about the density of an object and then test it in the column. How do the data support or not support the results?

When all the liquids and small objects have been added to your density tower, you will have what appears to be a "magic" column but it's all based on science. All of the liquids will be clearly distinguishable from each other and each of the objects will have settled at different levels within the column. Construct a table to show the order that the liquids and objects are in at the start. Be sure to record the date, too. If you leave it undisturbed over time, some interesting changes may occur in the column. Keep track of what you see with notes and photos with dates. Science fair anyone?

# data[].attributes.attachment_link.title
Amazing 9 Layer Density Tower - SICK Science! | Science Experiments | Steve Spangler Science

# data[].attributes.attachment_link.description
With this science-magic trick, you'll put a new spin on our famous Density Column demonstration. First, you'll discover how to stack nine layers of liquids on top of each other. That alone looks really cool, but then you take it up a notch by making different solid objects "float" in the middle of all those cool looking stacked liquids.

# data[].attributes.attachment_link.readable_text
In Maximum Capacity, you play the role of an elevator attendant who must bring as many gorillas as possible to the eighth floor for the annual Gorilla's Ball at the Jungle Hotel! The only problem is, the doors to the ball close in three minutes, and there are still hundreds of anxious gorillas waiting. Bring as many as you can to the eighth floor in three minutes. Check the weight capacity at the top of the elevator. It changes with each trip. Drag the gorillas into the elevator. Drag as many as you can without exceeding the weight capacity. You will have to use your quick addition, estimation, and number sense skills. The weight of each gorilla is listed on its hat, or, on its bag.

# data[].attributes.attachment_link.description
In Maximum Capacity, you play the role of an elevator attendant who must bring as many gorillas as possible to the eighth floor for the annual Gorilla's Ball at the Jungle Hotel! The only problem is, the doors to the ball close in three minutes, and there are still hundreds of anxious gorillas waiting.

# data[].attributes.headline
PDST Measures Manual: Eat Like a Bird p.149

# data[].attributes.subject
PDST Measures Manual: Eat Like a Bird p.149

# data[].attributes.attachment_link.description
There are four equal weights on one side of the scale and an apple
on the other side. What can you say that is true about the apple
and the weights from the picture?

# data[].attributes.attachment_link.readable_text
Grandma had made pies for a bake sale. She had carefully put equal amounts of mixture in each pie tin and was now trying to find the weight of the pies.

She had a problem; she only had one $200$ gram weight and one $125$ gram weight.

She found that one pie balanced on the scale with both weights and a quarter of a pie.

How heavy was each pie?

# data[].attributes.attachment_link.description
Grandma had made pies for a bake sale. She had carefully put equal amounts of mixture in each pie tin and was now trying to find the weight of the pies. She had a problem; she only had one $200$ gram weight and one $125$ gram weight.

# data[].attributes.headline
PDST Measures Manual: Bags of Weight p.145

# data[].attributes.subject
PDST Measures Manual: Bags of Weight p.145

# data[].attributes.headline
PDST Shape and Space Manual: Properties of Quadrilaterals p.108

# data[].attributes.subject
PDST Shape and Space Manual: Properties of Quadrilaterals p.108

# data[].attributes.attachment_link.description
The value of the circle changes in each of the following problems. Can you discover its value in each problem?

# data[].attributes.attachment_link.readable_text
Here are the six faces of a cube - in no particular order:

Here are three views of the cube:

Can you deduce where the faces are in relation to each other and record them on the net of this cube?

You might like to use this interactivity to keep track of your thinking. You can drag the picture of each face onto the net.

# data[].attributes.attachment_link.description
Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

# data[].attributes.attachment_link.readable_text
Please enable JavaScript in your browser to access Mathigon.
Something went wrong when loading this Polypad. Please try again later!
Keyboard Shortcuts and Accessibility

These are the keyboard shortcuts supported by Polypad for accessibility:

SHIFT: hold while you click on multiple tiles to select all of them at once

BACKSPACE: delete your current selection

C: duplicate your current selection

CTRL/CMD + X/Y: undo or redo your last change

ARROWS: move the currently selected tiles up, down, left or right (hold SHIFT to reduce the shift size, for more precise moving)

R: rotate the currently selected tile by 15° (hold SHIFT to rotate by -15°)

S: move the focus to the sidebar on the left

T: move the focus to the toolbar at the bottom

U: move the focus to the canvas area

ESC: clear the current selection and close any open popups and modals

TAB: cycle through all buttons on the page and tiles on the canvas (hold SHIFT to reverse direction)

Use CTRL/CMD + X/C/V to cut, copy or paste tiles. You can even copy and paste tiles from one canvas onto another!

Points and tiles will automatically snap to nearby shapes or gridlines as you move them. You can disable this behaviour by pressing the SHIFT key while moving an item with your mouse or trackpad.

You can learn more about our commitment to accessibility, as well as a WCAG checklist, at mathigon.org/accessibility

Generate Embed Code

You can embed a Polypad canvas on other websites like Wordpress: just select the features required below, and then copy the code block into the HTML of your website. We provide this service only for non-commercial, educational purposes. If you want to use Polypad commercially, please contact us.
It is impossible to balance these weights.

Image Upload Failed

Unfortunately, we couldn't upload this image. Make sure you are signed into your Mathigon account, and that the image is a PNG or JPEG file less than 1MB.

# data[].attributes.attachment_link.title
Polypad - Virtual Manipulatives - Mathigon

# data[].attributes.attachment_link.description
Virtual Manipulatives for Mathematics Classrooms: polygons, number and algebra tiles, fraction bars, tangram, pentominoes, and more.

# data[].attributes.attachment_link.description
Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.

# data[].attributes.headline
Khan Academy: Solving Problems with Pictograms

# data[].attributes.subject
Khan Academy: Solving Problems with Pictograms

# data[].attributes.attachment_link.title
Solve problems with picture graphs (practice) | Khan Academy

# data[].attributes.attachment_link.description
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

# data[].attributes.attachment_link.readable_text
Age 7 to 11 Challenge Level:

Class 4 was making graphs. Ben, Ali, Katie and Charlene decided to make graphs of the sizes of the seven classes in the school.

They went to the office to collect the numbers of children in all the other classes. Ben and Ali wrote down the numbers for Classes 1, 2 and 3. Katie and Charlene wrote down the numbers for Classes 5, 6 and 7. Of course they all knew the number of children in Class 4.

Ben and Ali drew a bar chart. It looked like this:

Katie and Charlene decided to make theirs differently. They drew this graph:

Miss Brown came along to look at their work.

"It's an interesting graph," she said, "but it's difficult to tell how many children are in each class. Please can you make a scale on it so we can all read it?"

Katie and Charlene did what they were told.

How many children were there altogether in Classes 5, 6 and 7?

# data[].attributes.attachment_link.description
Age 7 to 11 Challenge Level: Class 4 was making graphs. Ben, Ali, Katie and Charlene decided to make graphs of the sizes of the seven classes in the school. They went to the office to collect the numbers of children in all the other classes.

# data[].attributes.headline
Virtual Manipulative: Create your own graph

# data[].attributes.subject
Virtual Manipulative: Create your own graph

# data[].attributes.attachment_link.title
Graph Color | Teaching Tools | Toy Theater Educational Games

# data[].attributes.attachment_link.description
Free-style coloring tool to model arrays on a graph. Useful for teaching addition, subtraction, and multiplication.

# data[].attributes.attachment_link.description
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new

# data[].attributes.attachment_link.description
The value of the circle changes in each of the following problems. Can you discover its value in each problem?

# 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.readable_text
Five Steps to 50 printable sheet
This challenge is about counting on and back in steps of 1, 10 and 100.

Roll a dice twice to establish your starting number - the first roll will give you the tens digit and the second roll will give you the units digit.
You can then make five jumps to get as close to 50 as possible.
You can jump forwards or backwards in jumps of 1 or 10 or 100.

Compare your strategy with a friend.
Did you jump forwards or backwards?
Can you land on 50 exactly?
How far from 50 were you?
Could you do it another way?
Could you get even closer?
Which numbers can get you to 50?
Which can't?

Roll the dice again and have another go!

For example:
I roll a dice and get a 2 then a 3, so my starting number is 23.
I make the following jumps to get as close to 50 as possible:
Starting number is 23
Jump one is +10 to get me to 33
Jump two is +10 to get me to 43
Jump three is +10 to get me to 53
Jump four is -1 to get me to 52
Jump five is -1 to get me to 51

# data[].attributes.attachment_link.description
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?

# data[].attributes.attachment_link.description
How would you put these journey lengths in order? Give a bit of a place value challenge with subtractions set out not as a calculation.

# data[].attributes.attachment_link.readable_text
Here's a game to play with an adult!

How do you play?
You'll need an adult to play with.
You'll also need a 1 to 6 dice (you could use our interactive dice), and a grid like the one below. You can print some off here.

Take turns with the adult to throw the dice and draw that number of dots in one of the boxes on the grid. Put all of your dots in one of the boxes. You can't split them up and you can't have more than six dots in a box. When a box is full, you could put a tick in the corner like this:

Keep going until there are three ticks in a row or column or diagonal. The winner is the person who puts the last tick.

Now, can you change the game to make your own version?
How do you know where to put your dots?

There is a poster of the game here.

Notes for adults
The game as introduced is intended for KS1 children who are just beginning to become confident with small numbers. However there are many variations, some suggested below, that make it suitable for older children. Consolidation of basic number facts is combined with an element of strategic thinking.

Easier version: small children could use counters on a large grid. They could begin with six counters in each box and take away the number thrown on the dice.
Harder version: try using a different total, different dice, or a bigger grid. You could make the winner the first to complete a whole row that adds to a certain total (e.g. 20), change the shape of the grid (triangles rather than squares perhaps), or use a different sort of number - fractions, decimals, percentages...

There's a classroom version of this game here.

# data[].attributes.attachment_link.description
Here's a game to play with an adult! How do you play? You'll need an adult to play with. You'll also need a 1 to 6 dice (you could use our interactive dice), and a grid like the one below. You can print some off here.

# data[].attributes.attachment_link.readable_text
Base Ten Blocks (also known as "Base 10 Blocks" and "Place Value Blocks") is an online mathematical manipulative that helps students learn addition, subtraction, number sense, place value and counting. It lets them investigate how to regroup and solve problems with whole numbers and eventually fractions and decimals.

Overall, Base Ten Blocks provides a visual foundation for the abstract algorithms we want students to use as they grow.

# data[].attributes.attachment_link.title
Base Ten Blocks | Manipulatives | Coolmath4Kids

# data[].attributes.attachment_link.description
Base Ten Blocks virtual manipulative - a free online tool for classrooms and homes

# data[].attributes.attachment_link.readable_text
If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Video transcript

find the place value of 3 in 4356 now whenever I think about place value and the more you do practice problems on this will become a little bit of second nature but whenever I see a problem like this I like to expand out what 4356 really is so let me rewrite the number so if I were to write and I'll write it in different colors so 4356 is equal to and just think about how I just set it it is equal to four thousand four thousand plus 300 + 300 + 50 + 50 + six and you could come up with that just based on how we set it 4356 now another way to think about this is this is just like saying this is for thousands for thousands for thousands plus or you could even think of end so plus three hundreds three hundreds plus fifty you could think of it as five tens five tens plus six and instead of six we could say plus six ones plus six ones and so if we go back to the original number 4356 this is the same thing as four I'll write it down for let me see how well I can I'll write it up write this this is the same thing as four thousands for thousands three hundred three hundred five tens five tens and then six ones so when they ask what is the place value of 3 in 4356 we're concerned with this 3 right here and its place value it's in the hundreds place if there was a four here that would mean we're dealing with four hundred if there's a five five hundreds it's the third from the right this is the ones six ones five tens three hundred so the answer here is it is in the hundreds place it is in the hundreds place

# data[].attributes.attachment_link.title
Finding place value (video) | Place value | Khan Academy

# data[].attributes.attachment_link.description
If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

# data[].attributes.attachment_link.description
Official education portal of the Department of Education and Skills in Ireland. Curriculum focused resources and support for primary and post primary teachers.

# data[].attributes.headline
PDST Fractions Manual: Counting in Fractions p.97

# data[].attributes.subject
PDST Fractions Manual: Counting in Fractions p.97

# data[].attributes.attachment_link.readable_text
Students often struggle with the concept of fractions. This interactive fraction strips tool helps students visualize fractions. With these online fraction strips, students can model fractions, solve fraction problems, explore equivalent fractions, and observe the differences between denominators.

To use the interactive fraction strips tool, click and drag the strips onto the canvas. You can drag as many of each fraction as you'd like. To remove the strips, drag them off the canvas. Change the chart to accommodate two whole units by pressing the "Unit Double" button. Add annotations using the pencil tool and erase using the eraser. To clear the canvas, press the trash can button.

A few activities you can do with students while using the online fraction strip tool include:

Have students model a given fraction, mixed or not. For example 1 1/4 or 3/6.

Ask students to model addition, subtraction, multiplication, or division problems using the fraction strips.

Ask students to find equivalent fractions for a certain fraction. For example, how many sixths are equivalent to 1/3?

Ask students to use the pencil tool to divide one of the wholes on the chart into fourths. Then, students can check their work by dragging fourths onto the chart afterward.

Looking for more fraction manipulatives? Try our interactive fraction circles.

Visit classplayground.com for more resources and printables about fraction strips.

# data[].attributes.attachment_link.title
Fraction Strips | Free Virtual Manipulatives | Toy Theater

# data[].attributes.attachment_link.description
Use the interactive fraction strips tool to help students visualize, model, and explore fractions. Students can also solve problems using fraction strips.

# data[].attributes.attachment_link.readable_text
Students explore folding paper shapes into equal parts and labelling the parts with written fractions.

Select the shapes to be used according to the type of fraction being studied. Rectangles and thin strips are suitable for all fractions. Circles and triangles are less versatile.

Ensure students understand whether they are dividing into equal areas or equal lengths.

Constantly emphasise the importance of the parts being equal in size. Ask students to explain how they know they have actually represented the particular fraction correctly.

For shapes and fractions that are too difficult to divide by folding (e.g. folding a circle into thirds), students can estimate where to draw the dividing lines. They can then cut out the parts, and directly compare the areas.

Use questioning and discussion to prompt students to realise that:

the same fraction can be represented in a variety of ways, often by dividing the same shape in different ways

the same shape can be used to model a variety of different fractions.

# data[].attributes.attachment_link.description
Students explore folding paper shapes into equal parts and labelling the parts with written fractions. Select the shapes to be used according to the type of fraction being studied. Rectangles and thin strips are suitable for all fractions. Circles and triangles are less versatile.

# data[].attributes.attachment_link.description
Official education portal of the Department of Education and Skills in Ireland. Curriculum focused resources and support for primary and post primary teachers.

# data[].attributes.attachment_link.readable_text
Odd One Out activities are suitable for all age groups. By encouraging all pupils to 'have a go' and 'valuing all contributions', the skills of reasoning, communicating and expressing are developed. Success is based on skills rather than answers. It also allows every pupil to partake in the activity, no matter what their ability.

Examples of questions/prompts to promote classroom discussion:
● Which one do you think is the odd one out?
● Give me a reason.
● Try to give me another reason why that one might be odd.
● Who had a different answer?
● Give me a reason why each one might be the odd one out.

Take a look at this short video from our 'STEM in a Bubble' webinar which explores 'Odd One Out' activities further. A complete recording of this webinar along with the resources referenced is available here.

Below you will find some Odd One Out stories to try with the pupils in your class. For more examples, see http://wodb.ca/

Choose an Odd One odd activity below. These resources are available in Irish and English in the downloadable file. To download the activity, simply click on the picture.

Choose an Odd One odd activity below. These resources are available in Irish and English in the downloadable file. To download the activity, simply click on the picture.

Either your browser does not support JavaScript or it is disabled. Scoilnet.ie works best with JavaScript enabled.
Add a resource

To get the best possible experience using our website we recommend that you upgrade to a newer version or other web browser.
Upgrade your browser now

What you need...

To register for a Scoilnet Account you will need to have a Teaching Council number and a roll number for your school in Ireland.

If you already have a Scoilnet Account then you can sign in here.

The benefits...

A Scoilnet account will allow you to upload your resources or weblinks to Scoilnet as well as enabling you to share and add resources to a favourites listing. Users who have a Scoilnet Account will also be able to fully access Scoilnet Maps and Census@School from home.

# data[].attributes.attachment_link.description
Official education portal of the Department of Education and Skills in Ireland. Curriculum focused resources and support for primary and post primary teachers.

# data[].attributes.attachment_link.description
Have a look at these photos of different fruit. How many do you see? How did you count?

# data[].attributes.attachment_link.title
Keeping the Learning Going At Home: Card Games

# data[].attributes.attachment_link.description
In this series, specially written for Independent.ie, the Professional Development Service for Teachers (PDST), offers some valuable pointers to parents across a range of different learning areas. PDST is a Department of Education and Skills support service.

# data[].attributes.attachment_link.readable_text
Maze 100 printable sheet
In this maze there are numbers in each of the cells. You go through adding all the numbers that you pass. You may not go through any cell more than once.

Can you find a way through in which the numbers add to exactly 100?

What is the lowest number you can make going through the maze?

What is the highest number you can make going through the maze? (Remember you may not go through any cell more than once.)

# data[].attributes.attachment_link.description
Can you go through this maze so that the numbers you pass add to exactly 100?

# data[].attributes.attachment_link.description
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

# data[].attributes.attachment_link.readable_text
Unfortunately many Flash resources no longer work as Adobe have blocked Flash content from running in Flash Player from 12 January 2021. Sorry for any inconvenience caused.

For more information see Adobe's Flash Player End of Life Information page.

All of Topmarks' own authored resources still work as none are based upon Flash. We are working hard to create more free resources for you.

We have managed to keep a selection of the Flash based resources that we host with permission working without the need to have Flash Player installed.

Return to our home page.

# data[].attributes.attachment_link.description
Unfortunately many Flash resources no longer work as Adobe have blocked Flash content from running in Flash Player from 12 January 2021. Sorry for any inconvenience caused. For more information see Adobe's Flash Player End of Life Information page. All of Topmarks' own authored resources still work as none are based upon Flash.

# data[].attributes.attachment_link.description
Daily 24 Puzzle For Maths Week 2020 we have two daily 24 puzzles. In response to the Covid-19 alert we began presenting a daily puzzle and they were so popular we ran them for 4 months. Now, they are back by popular demand. 24 is a good

# data[].attributes.attachment_link.readable_text
Jennie the old sheep dog is lazing around in the paddock near the house.

She counts the number of animals in the paddock. There are 11 of them, pigs and ducks.

Then she counts the legs. She sees 28 legs.

How many ducks are there?

Specific Learning Outcomes

Solve a story problem using multiplication facts of 2 and 4.

Devise and use problem solving strategies (guess and check, guess and improve, act it out, draw a picture)

Description of Mathematics

This problem uses the multiplication facts of 2 and 4. It also gives students the opportunity to combine the operations of addition and subtraction. As there are many ways to solve this problem it is accessible to a range of students.

Required Resource Materials

The Problem

Jennie the old sheep dog is lazing around in the paddock near the house. She counts the number of animals in the paddock. There are 11 of them, pigs and ducks. Then she counts the legs. She sees 28 legs.
How many ducks are there?

Lesson Sequence

1. Read the problem to the class.

2. Ask the students to highlight the important information.

3. For beginning problem solvers you might like to use them to act out the problem.

4. Start with 4 students at the front of the room. Ask 2 of them to be pigs (on all 4's) while the other 2 stand (ducks). Ask the class to count the legs.

5. Ask the students to think about what would happen if you "turned" one of the pigs into a duck. How many animals? How many legs?

6. Brainstorm other ways to solve the problem - list possibilities on board (draw, equipment, guess)

7. Students solve the problem.

8. Sharing of solutions and the strategies used.

Extension

Get the students to write and solve their own problems by changing the numbers of animals and legs.

Other contexts for the problem

Horses and riders
Tricycles and bicycles

Solution

3 pigs, 8 ducks

There are many ways to do this problem. For instance, it is a good problem to introduce the use of a table and to use it for guess and improve. If the first guess was 5 pigs and 6 ducks there are 32 legs. At this point the students should realise that to reduce the number of legs we have to reduce the number of pigs. Some students may be able to reason that when you reduce the pigs by one and add a duck you have reduced the number of legs by 2.

# data[].attributes.attachment_link.description
Jennie the old sheep dog is lazing around in the paddock near the house. She counts the number of animals in the paddock. There are 11 of them, pigs and ducks. Then she counts the legs. She sees 28 legs. How many ducks are there?

# data[].attributes.attachment_link.description
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

# data[].attributes.attachment_link.readable_text
An interactive place value and decimals display.

Aimed at children 8yrs and older.

Learning Objectives:

Y3:

To count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10

Pupils connect tenths to place value, decimal measures and to division by 10.

Y4:

To count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.

Pupils should connect hundredths to tenths and place value and decimal measure

Ways to use it:

Partition:
Press on each card to partition. What is the value of this digit?

Hide & Count:
Hide the numbers, the teacher adds tenths, hundreths etc. When the teacher stops ask the children to write the number on their drywipe boards.

Count Backwards:
Start from 1 and count backwards in tenths or hundredths.

Count Forwards:
Start from 99.90 and count forwards in hundredths.

Build on the learning with
these games:

This game is © copyright 2019, J.Barrett, ictgames.com All Rights Reserved.

Made using the and libraries.

# data[].attributes.attachment_link.description
Aimed at children 8yrs and older. Y3: To count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10 Pupils connect tenths to place value, decimal measures and to division by 10.

# data[].attributes.attachment_link.readable_text
For students, decimals are often a challenging concept to grasp. This interactive decimal strips tool helps students model and visualize decimals. When using the online decimal strips tool, students can model, explore, and compare decimals. Additionally, the decimal strips are a useful interactive tool for modeling and solving operations involving decimals.

Using the interactive decimal strips tool is easy. Simply drag the decimal strips on or off the canvas. Modify the chart so that two whole units can be displayed by clicking on the "Unit Double" button. Write on the canvas using the pencil button and click on the eraser symbol to erase. To clear the whole canvas, click on the trash can symbol.

Here are a few suggestions for using the interactive decimal strips tool:

Ask students to model a given decimal such as .25 or .70

Ask students to model and solve an operation involving decimals.

Invite students to drag various decimals onto the canvas and compare their values. You can even have students write statements using , and = signs.

Visit classplayground.com for related decimal printables such as strips, decimal place value charts, and more.

# data[].attributes.attachment_link.title
Decimal Strips | Free Virtual Manipulatives | Toy Theater

# data[].attributes.attachment_link.description
This interactive decimal strips tool brings the topic to life so students can visualize, model, and explore decimals. Plus, it's free!

# data[].attributes.attachment_link.description
This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.

# data[].attributes.attachment_link.readable_text
Odd One Out activities are suitable for all age groups. By encouraging all pupils to 'have a go' and 'valuing all contributions', the skills of reasoning, communicating and expressing are developed. Success is based on skills rather than answers. It also allows every pupil to partake in the activity, no matter what their ability.

Examples of questions/prompts to promote classroom discussion:
● Which one do you think is the odd one out?
● Give me a reason.
● Try to give me another reason why that one might be odd.
● Who had a different answer?
● Give me a reason why each one might be the odd one out.

Take a look at this short video from our 'STEM in a Bubble' webinar which explores 'Odd One Out' activities further. A complete recording of this webinar along with the resources referenced is available here.

Below you will find some Odd One Out stories to try with the pupils in your class. For more examples, see http://wodb.ca/

Choose an Odd One odd activity below. These resources are available in Irish and English in the downloadable file. To download the activity, simply click on the picture.

Choose an Odd One odd activity below. These resources are available in Irish and English in the downloadable file. To download the activity, simply click on the picture.

Either your browser does not support JavaScript or it is disabled. Scoilnet.ie works best with JavaScript enabled.
Add a resource

To get the best possible experience using our website we recommend that you upgrade to a newer version or other web browser.
Upgrade your browser now

What you need...

To register for a Scoilnet Account you will need to have a Teaching Council number and a roll number for your school in Ireland.

If you already have a Scoilnet Account then you can sign in here.

The benefits...

A Scoilnet account will allow you to upload your resources or weblinks to Scoilnet as well as enabling you to share and add resources to a favourites listing. Users who have a Scoilnet Account will also be able to fully access Scoilnet Maps and Census@School from home.

# data[].attributes.attachment_link.description
Official education portal of the Department of Education and Skills in Ireland. Curriculum focused resources and support for primary and post primary teachers.

# data[].attributes.attachment_link.description
The Returning to School Curriculum Guidance for Primary School Leaders and Teachers document, which can be accessed by clicking on the image, explains that “while the use of physical manipulatives may be more restricted owing to health and safety and hygiene requirements, alternative versions of

# data[].attributes.headline
PDST Maths Game: Nice or Nasty and Catalogue Trail

# data[].attributes.subject
PDST Maths Game: Nice or Nasty and Catalogue Trail

# data[].attributes.attachment_link.title
Largest Difference - an ATM 'Maths Snacks' video

# data[].attributes.attachment_link.readable_text
These general interactive resources can be used in a variety of contexts in the primary classroom to support learners working on mathematics.

Interactive tasks and games

These primary activities and games all have interactive content, making them ideal for use on tablets, laptops or in a computer room.

# data[].attributes.attachment_link.description
These general interactive resources can be used in a variety of contexts in the primary classroom to support learners working on mathematics. These primary activities and games all have interactive content, making them ideal for use on tablets, laptops or in a computer room.

# data[].attributes.attachment_link.readable_text
Here you can simulate throwing dice and spinning spinners.

Click on the purple cog in the top right of the interactivity to change the settings.

You can decide on the range of numbers on your dice or spinner (1-6 or 0-9), and you can roll/spin two or three at a time if you wish. There is also an option to see dots rather than numerals on the dice.

# data[].attributes.attachment_link.description
Simple dice and spinners tool for experiments.

# data[].attributes.headline
PDST Place Value, Decimals and Percentages Manual p.58: Win a One Game

# data[].attributes.subject
PDST Place Value, Decimals and Percentages Manual p.58: Win a One Game

# data[].attributes.attachment_link.readable_text
Have you noticed that some very long numbers are very big whilst other very long numbers are small? Can you think of an example of each?
Here's a game where you can test your skill at putting small numbers into the right order - it's not as easy as it sounds!

How to play
You need a partner, a copy of the game board, and two different coloured pencils.
Decide who goes first.
Take turns to choose a number from the grid and mark it on the spiral. Make sure you know where 0 and where 1 is!
Keep taking turns until one of you has marked three numbers next to each other.

What next?
Can you work out a winning strategy?
Does it matter who goes first?
Does it matter which number you choose first?

Can you make up a different set of numbers which would make the game more challenging?
Perhaps you could have different start and end numbers for your spiral?
Send us your ideas so that we can share them with other children.
You may be interested in the other problems in our Fractions Unpacked Feature.

# data[].attributes.attachment_link.description
Have you noticed that some very long numbers are very big whilst other very long numbers are small? Can you think of an example of each? Here's a game where you can test your skill at putting small numbers into the right order - it's not as easy as it sounds!