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PMC - Fractions Suggestions for Teaching (PDF)

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PMC - Fractions Suggestions for Teaching (PDF)

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PMC - Suggestions for Children's Learning

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PMC - Suggestions for Children's Learning

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Suggestions for the Learning Environment

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Suggestions for the Learning Environment

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PMC - Oide - Welcome to the Primary Mathematics Curriculum Hub

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PMC Videos Introduction

Welcome to our PMC in Action page, where you have a front row seat to witness the incredible learning experiences of pupils from various school contexts across Ireland. Immerse yourself in a captivating collection of videos that showcase real-life examples of pupils learning. Join with us as we celebrate these amazing classroom environments, innovative teachers and the genuinely enthusiastic pupils interacting with the PMC.

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Welcome to our PMC in Action page, where you have a front row seat to witness the incredible learning experiences of pupils from various school contexts across Ireland.

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Explore fractions while you help yourself to 1/3 of a chocolate cake and wash it down with 1/2 a glass of water! Create your own fractions using fun interactive objects. Match shapes and numbers to earn stars in the fractions game. Challenge yourself on any level you like.

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Build fractions from shapes and numbers to earn stars in this fractions game or explore in the Fractions Lab. Challenge yourself on any level you like. Try to collect lots of stars!

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Learn what fractions look like on the number line, and get to see Equivalent Fractions easily.

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Match shapes and numbers to earn stars in this fractions game. Challenge yourself on any level you like. Try to collect lots of stars!

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Explore fractions while you help yourself to 1 and 1/2 chocolate cakes and wash it down with 1/3 a glass of water! Create your own fractions using fun interactive objects. Match shapes and numbers to earn stars in the mixed number game. Challenge yourself on any level you like.

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Unleash your creativity with the world's best virtual manipulatives!

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Slice a pizza, and we get fractions:

The top number says how many slices we have.
The bottom number says how many equal slices the whole pizza was cut into.

Have a try yourself:

Equivalent Fractions

Some fractions may look different, but are really the same, for example:

=

=

(Four-Eighths)

(Two-Quarters)

(One-Half)

=

=

It is usually best to show an answer using the simplest fraction ( in this case ). That is called Simplifying, or Reducing the Fraction

Numerator / Denominator

We call the top number the Numerator, it is the number of parts we have.
We call the bottom number the Denominator, it is the number of parts the whole is divided into.

You just have to remember those names! (If you forget just think "Down"-ominator)

Adding Fractions

It is easy to add fractions with the same denominator (same bottom number):

Another example:

Five-eighths plus one-eighth equals six-eighths, equals three-quarters

Adding Fractions with Different Denominators

But what about when the denominators (the bottom numbers) are not the same?

Three-eighths plus one-quarter equals ... what?

We must somehow make the denominators the same.

Three-eighths plus two-eighths equals five-eighths

There are two popular methods to make the denominators the same:

(They both work nicely, use the one you prefer.)

Other Things We Can Do With Fractions

We can also:

Visit the Fractions Index to find out even more.

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The top number says how many slices we have. The bottom number says how many equal slices the whole pizza was cut into. Some fractions may look different, but are really the same, for example: = = (Four-Eighths) (Two-Quarters) (One-Half) = = It is usually best to show an answer using the simplest fraction ( in this case ).

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23/11/17 - new version added. This version is tablet friendly and can be played directly on any device.

Drag the flag to the correct position on a number line. Lots of choice over level, including whole numbers, negative number and decimals. Can be used to teach place value, approximation skills, and reading varying scales.

Choose one type of number line or for more of a challenge you can select several. Work quickly to get more time, build your score and climb up the leaderboard.
For more resources involving partitioning and place value click here.
Scan to open this game on a mobile device. Right-click to copy and paste it onto a homework sheet.

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Placing Numbers on a Number Line - Tablet Version

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Drag the arrow to the correct point on a number line. Lots of choice over level, inculding whole numbers, negative number, decimals, fraction and multiples.

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it may be more appropriate to present ideas and tasks without the ppt offered (where they are)

ppts are provided with, hopefully, some interesting questions and so that teachers can adapt questions

sorry, I'm a unicase fan...

contents have been moved to this blog

apologies if this causes any difficulties e.g. with links

practice and GCSE sheets blog

ideas are aimed at those who teach mathematics to adolescents; who like tasks with some depth, novelty and a focus on generalising relationships and on transformationdon steward

MEDIAN

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it may be more appropriate to present ideas and tasks without the ppt offered (where they are) ppts are provided with, hopefully, some interesting questions and so that teachers can adapt questions sorry, I'm a unicase fan... contents have been moved to this blog apologies if this causes any difficulties e.g.

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Fraction walls are a great way to teach about fractions and in particular equivalent fractions. In a fraction wall each row or layer of the wall represents one whole number. The layers are divided into a number of bricks and hence each brick represents a fraction whose denominator is equal to the number of bricks in that layer. Each brick can be turned on or off by clicking it. This wall also allows the display of decimal and percentage values. To the right of the wall are boxes which can be hidden, the value of each box is fraction of the wall that has been turned on.

Selecting different walls

When you launch this interactive teaching program the initial wall is a mixed one showing 3 distinct fraction families. Change the wall by using the mode control. 'Large' displays a wall in which the layers are split 1,2,3 up to 12. The others split the wall along 2s, 3s or 5s. The 5s also includes a lower wall of 100 bricks, this naturally works quite well in explaining percentages since each brick represent ¹⁄ ₁₀₀ or 1%.

Fractions, decimals or percentages

Use the display type control to display decimals (rounded to 2dp), percentages (rounded to 1dp), fractions or none.

The equivalent fraction control

Normally when you click a brick to turn it on or off, only that brick is affected. However if you turn on the equivalent fraction function by clicking the 'Eq' toggle button. Now when a brick is clicked the other layers will turn on bricks if they can match an equivalent fraction. Note, this is not always possible, in fact if you select the primes wall it is never possible to show an equivalent fraction. In this case all the other layers have bricks turned off.

Least Common Multiple

Also known as 'the lowest common multiple' or 'smallest common multiple' is crucial when adding, subtracting or comparing fractions. This button will calculate the LCM based on the rows that have active bricks. Pressing the LCM button will create a new wall that contains the originally selected fraction but also a new layer with the number of divisions equalling the least common multiple of the denominators of the other rows. Sounds complicated, but it really just means that it is always possible to create an equivalent fraction in the LCM row from the other rows.

Other controls

The other controls are

'On' button when clicked will turn on all the bricks

'Off' button when clicked will turn off all the bricks

'Random' button creates a randomized wall in which roughly half the bricks are on. Usually you would hide the totals before pressing this and then the class can work out each fraction in the random wall.

' < ' button will align all the bricks to the left hand side of the wall. This is often pressed after using the randomize function. Fractions can then be compared by considering the length of each row of on bricks.

hide totals click to hide all the totals. The individuals total can then be clicked to show the value.

show totals reveal all the totals.

Advanced Section

To show or hide the advanced section click the advanced toggle button

When the advance controls are on, each layer of the wall has a dedicated slider, move this to change the number the number of bricks in that layer.

Automatic 1 button when clicked create a new wall by dividing the top layer by all its ascending prime factors. So for example if you move the top slider so the top layer has 42 bricks and then click the button. The primefactors of 42 are 2,3 and 7. So the second layer will have 42÷2=21 bricks, the third layer will have 21÷3=7 bricks and the final layer will have 7÷7= 1 brick.

Automatic 2 is similar but creates a layer for every factor of the top layer value.

Add Layer adds a new layer to the bottom of the wall.

total type select control will change the type of total to display. The default is to match what the wall shows, so in this case if the wall is showing fraction the total will be a fraction. But using this control it is now possible for fractions to be shown in the wall but the total to be given as a percentage.

Further fractions

Closely related to this activity is the percentage fraction and decimals grid, which can be used to display a square or circle fraction representation.

Other activities that can be used to teach fractions are the clock activity which uses the clock face to show the fraction of minutes passed in an hour. Launch the activity and select the fractions mode, this mode also show equivalent fractions for example ³⁰⁄ ₆₀ = ¹⁄ ₂. The number explorer activity can show the fraction resulting from division of a number.

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Interactive Fraction Wall | online fraction | percentage | decimal | visnos

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Online fraction wall, easily display fractions using interactive white board. Simple to explore fraction,decimals and percentages . Step by step view equivalent fractions. Beautiful display which children love.

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PMC - Fractions - The Progression Continua

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PMC - Fractions - The Progression Continua

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PMC - Fractions - Suggestions for Learning at Home

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PMC - Fractions - Suggestions for Learning at Home

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Practice fractions with our popular math games. Learn about equivalent fractions, adding and subtracting fractions, multiplying fractions and more.

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Thinking Blocks - Fraction Problem Solving

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Thinking Blocks - Fraction Problem Solving

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Essential Skills

Problem Solving - model and solve word problems

Common Core Connection for Grades 3, 4 and 5

Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
Join and separate parts referring to the same whole.
Solve word problems involving addition and subtraction of fractions
referring to the same whole and having like denominators.
Solve word problems involving multiplication of a fraction by a whole number.

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Model and solve word problems using interactive tape diagrams.

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Steve Wyborney\\\'s Blog: I\\\'m on a Learning Mission.

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Tiled Area Questions are designed to provide students with the opportunity to compose and decompose numbers. This post primarily focuses on fractions. If you are a K-2 teacher, you may really like this version.

Watch the video, download the resources, and give your student the opportunity to visualize, decompose, compare, and compose numbers.

Click here to download the 12 Colored Displays.

Click here to download the 12 Combination Displays.

Click here to download the 12 White Printables

Click here to download the 12 Pages With 6 Identical Images.

I encourage you to give your students opportunities to see the same concept in many different ways.
NEW TILE POSTS IN THIS SERIES
The K-2 post is ready!!! Visit it here: Primary Tile Questions

The latest post in the series is ready: 3 Powerful Tile Strategies (and 40 New Downloadable Pages)

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

Many thanks to Melissa D. for sharing these pictures from her 7th grade classroom in Toronto. You can follow Melissa on Twitter @Dean_of_math .

Update: Melissa's excellent, beautiful blog post, "Embracing the struggle (aka #mathismore than a word problem)" is well worth your time, and will give a glimpse into her personal journey as well as how she is using Tiled Area Squares in her classroom. Take a look at her blog post with additional images .

Here is a sneak peak at Melissa's post. Click on either picture to see her post.

Thank you, Melissa, for sending these additional pictures as well.!
The Maze Hundreds Chart Provide Massive Space to Notice How to make Quick Subitizing Images + 3 Free Resources
I also recommend viewing these posts:

This post includes 50 (fifty!) animated number sense lessons for K-12 teachers.

Color the Cube Connectors (more downloadables and strategies)

Thank you for visiting my blog. Remember, if you have pictures of pages of student thinking that you would like to see on the blog, please send them to me.

All my best,

Steve

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Tiled Area Questions - Steve Wyborney's Blog: I'm on a Learning Mission.

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Tiled Area Questions are designed to provide students with the opportunity to compose and decompose numbers. This post primarily focuses on fractions. If