Challenge learners to create lines for a partner that they need to draw relevant fractional lengths for. Include all the examples in the lesson: 1/2, 1/3, 1/4, 1/5.

Provide manipulatives - unit cubes or some such small resource that can be used repeatedly to build a length - for learners who lack confidence with fractions. When learners line up the resources against each of the lines, they should be able to more easily 'break off' a half or other fraction to see what would be left. 

Then, learners could compare what they have left to the lines or draw a line about that length, from the questions.

Teacher guide

Presentation for What is a Fraction?

Pizza fractions

Images for fractions for four corner game

I can say how many parts make up a whole.

Revisit fractions of shapes to review the different fraction words. Following this, instruct Marty to walk a line and then instruct Marty to walk a fraction of that distance. Have learners measure both distances and think about how they compare.

Open the Marty the Robot app and build the code from the teacher guide into the workspace.

This code will have Marty walk a set number of steps and then walk a fraction of the first distance. You need to enter the values manually before running the code. 

Save this code in the app and give it an appropriate name. Please consult the teacher guide for step-by-step instructions for building it.

Share with learners the objectives and success criteria for the day's lesson, from slide 2 of the presentation in the resource section; perhaps display this before the lesson starts and keep it displayed until another slide is needed. 

Tell learners that they are going to play the four corners game. 

Below is the procedure for the four corners game

1. In each corner of the room is a fraction picture.

2. You will cover your eyes and allow learners to choose one of the corners and go it.

3. You will call out a fraction: half, third, fourth/quarter or fifth.

4. Learners who are in that corner are 'out' and need to sit in the middle of the room or off to the side.

5. The game continues until one or two learners are left.

The goal is to remind learners about the comparative size of fractions, taken from the same whole.

Have learners remind you of fractions that they know and what it means to be a fraction. 

Learners may suggest half, quarter, third and fifth, from the warm-up activity. Some learners may suggest other ones as well. Learners may suggest that, "A fraction is a part of something; fractions are all the same size, so my half is the same as your half; fractions make up a whole." 

Take time to question what learners mean by their statements; there may be some confusion with what they have remembered.

display slide 3 of the presentation, which shows rectangles being cut along the long edge, there are 4 examples for the 4 fraction pizza images.

display slide 4 of the presentation, which shows lines being cut and organised in parts

highlight how many parts make the whole for both slides: a half needs two parts to make a whole; a third, three; a quarter/fourth, four; etc.

Ask learners if they would like to estimate about how long part of a line is. Slide 5 of the presentation presents a number of different lines and fractions that can match with them. By exiting the presentation mode, learners will be able to drag fractional lines to go with the 'whole' line. 

Display Marty and inform learners that Marty is going to walk a distance and then Marty will walk a fraction of that distance. 

Place an x on the ground where Marty is to start, this could be with tape or a pencil/pen mark on a piece of paper stuck to the ground. 

After Marty walks a 'whole' distance, mark the stopping point and have a volunteer measure the distance to the nearest unit. 

Choose the fraction of the whole distance Marty will walk, on the app, and press that code block. 

Have learners look to see 'about' how much of the distance Marty walked, 

encourage the use of about when learners answer: 

I think it is about half, a third/fourth/quarter/fifth of the whole distance.

Tell learners how many times Marty will need to walk the fractional distance to walk the full distance, this will reinforce what the fraction means when compared to the whole

Because Marty is walking in the real world, different surfaces using the same code will affect the distance they travel

Share with learners the practice activity in the workbook, in the resources section, which shows a collection of Martys walking a distance, with a line trailing behind. For each question, learners need to identify which of the lines goes with which fraction name for the original. It is hoped that learners will quickly realise that a half is more than a third, which is more than a fourth/quarter, which is more than a fifth but initially, learners will line up the lines with a measuring tool to compare the lengths. 

As the activity questions continue, the challenge will increase: learners will have more choices than there are fraction lines. 

Bring learners back together to discuss what they found interesting about fractions. 

How did you make sure your fraction line was accurate?

What did you notice about the number on the bottom of the fraction?

What do you think will happen as the bottom number continues to increase?

A device with MartyBlocks to show the fraction lengths in action

Workbook for What is a Fraction

Use Marty to walk a distance, then walk a fraction of that distance

TEKS - Elementary Technology Applications: Kindergarten to Grade 2

Curriculum for Excellence - Technologies: Craft, Design, Engineering and Graphics

Curriculum for Excellence - Technologies: Computing Science

National Curriculum - Computing, Design and Technology: Design and Technology

Australian Curriculum - Mathematics: Measurement and Geometry – Geometric reasoning

Curriculum for Excellence - Health and Wellbeing: Relationships

Curriculum for Excellence - Technologies: Technological Developments in Society and Business

Next Generation Science Standards - Earth and Space Sciences:

National Curriculum - Science KS2: Physics – Light

Curriculum for Excellence - Science: Planet Earth 

CSTA Education Standards

National Curriculum - Mathematics KS2: Number - fractions

National Curriculum - Mathematics KS2: Geometry – properties of shapes

Curriculum for Excellence - Technologies: Digital Literacy

Curriculum for Excellence - Science: Materials

Common Core - Mathematics:

Curriculum for Excellence - Numeracy: Information Handling

National Curriculum - Science KS4: Chemistry – Earth and atmospheric science

Australian Curriculum – Digital Technologies, Design & technologies: Design & Technologies

Curriculum for Excellence - Literacy & English: Listening and Talking

Curriculum for Excellence - Science: Forces, electricity and waves

Australian Curriculum - Science: Science as a Human Endeavour

Curriculum for Excellence - Health and Wellbeing: Physical Activity and Sport

Curriculum for Excellence - Health and Wellbeing: Mental, Emotional, Social and Physical Wellbeing

Curriculum for Excellence - Numeracy: Number, Money and Measure

Curriculum for Excellence - Health and Wellbeing: Planning for Choices and Changes

TEKS - Elementary Science: Knowledge and Skills

Curriculum for Excellence - Numeracy: Shape, Position and Movement

Australian Curriculum - Mathematics: Number and Algebra - Fractions and decimals

National Curriculum - Science KS3: Physics – Motion and Forces

Australian Curriculum – Digital Technologies, Design & technologies: Digital Technologies

National Curriculum - Computing, Design and Technology: Computing

Curriculum for Excellence - Literacy & English: Reading

Next Generation Science Standards - Science and Engineering Practices:

Australian Curriculum - Science: Science Understanding - Physical Sciences

Next Generation Science Standards - Physical Sciences:

Curriculum for Excellence - Literacy & English: Writing

TEKS - Elementary Math: Knowledge and Skills

International Society for Technology in Education (ISTE)

Mathematics - Middle Years - Lesson 3 - What is a fraction

Challenge learners to create different lines - use a ruler to draw various line lengths - and identify where the fraction should lie on that line.

Encourage learners to use a ruler to draw the 1/3, 1/4 and 1/5 lengths from the activity page onto a scrap piece of paper. Once they draw this, they could use the drawn line to support finding where multiples of that fraction could sit on the line. Encourage learners to rely on the support page less as they progress through the activity page.

Presentation for Fraction Number Lines

I can compare fractions on a number line​.

I can compare unit and other proper fractions.

This lesson is about comparing fractions within the same whole. 

is 1/2 from 1/3? Use Marty to quickly illustrate the difference between fractions of a whole then use Marty to compare fractions with different wholes.

Open the Marty the Robot app and build the following piece of code into the workspace:

This code will have Marty walk a set distance and then walk a fraction of the first distance. You need to enter the values manually for how many steps, the initial step length and the first fraction before running the code. 

Share with learners the objectives and success criteria for the day's lesson, from slide 2 of the presentation in the educator resource section; perhaps display this before the lesson starts and keep it displayed until another slide is needed. 

Tell learners that they are going to play What Time is it Mr Wolf

1. One person is chosen to be 'the Wolf'.

2. Learners who are not the wolf call out, "What time is it, Mr Wolf?" The title can be changed: Mr need not be used.

3. The wolf calls out number from 1-12, followed by o'clock.

4. Learners count to the number as they step to the wolf.

5. This repeats until a learner either touches the wolf or the wolf shouts dinner time and tries to catch the children. If the catch one, they swap places.

To tie into today's lesson, stop the game mid way through and ask learners, "Can anyone tell me if they think they are about half way to the wolf (or the learner's name)?" Repeat with, "Can anyone tell me if they think they are less than half way to the wolf?" or, "more than half way?" Do this a couple of times as the different rounds unfold.

The goal is to remind learners about estimating, in this case half a distance.

Have learners remind you about the value of fractions. The might suggest that a half is more than a fourth/quarter or a fifth is less than a third; additionally, they may offer that it takes two halves to make a whole, or similar statements with other fraction quantities.

Display slide 3 from the presentation, it shows a line with a 0 on the far left and a 1 on the far right. The notes at the bottom of the presentation will guide a discussion but the goal is to determine good estimates of where fractional values would sit between 0 and 1, on a number line. If you would prefer to have a number line on a chalk board or whiteboard, please do so.

Draw attention to the fact that all of these fractions have a one for what is called the numerator - the number on the top of the fraction. The numerator tells me how many pieces of a fraction I have. The number on the bottom is the denominator - this tells me how many pieces I need to make a whole. 

Say, "For one half, I have one piece out of two that I need to make a whole; so, when I add a half more, I have two halves, which is the same as a whole. Let's look at the other fractions. This is what the number two halves looks like: 2/2."

The presentation on slide 4 illustrates how unit fractions are used to build other proper fractions with the same denominator. There are some animations that extend the unit fractions to show what increasing the numerator does to the value of the fraction.

Slide 5 shows a number line with a series of question marks. 0, 1/2 and 1 are marked on the number line to give learners a benchmark for comparing their estimates. Take plenty of time asking why learners think what they do about the estimates they give and how they go about deciding which fraction is more than another. The next value to be revealed is the biggest question if you want learners to make estimates about how much each question mark represents.

Present Marty to learners. Enter a value into the code that you prepared before the lesson for the number of steps, keep in mind that each step is about one inch so it would be good to have Marty walk at least 20 or so steps to better illustrate a fractional distance: having Marty take 5 steps will result in fractional distances that are very close in terms of value: 1/2 the distance would be about 6 cm / 2.5 in, 1/5 the distance would be about 2.5 cm / 1 in; 1/4 and 1/3 are very difficult to distinguish. Also include the fractional amount that Marty is to walk, we recommend entering 1/2 for the second time Marty walks and then other fractions suggested by learners to address thirds, quarters/fourths and fifths.

After Marty walks the last fractional distance, ask learners, "What do you think will happen if I press to run this program again?" 

If the last press had been for 1/5, move the green card to the 1/5 mark and place Marty down there. Marty will walk another fifth but not the combined distance is 2/5, mark this beside Marty's stopping point. If you want, repeat this until Marty reaches 1.

Below are suggestions for how to demonstrate Marty and for a video of the process of marking the floor indicating the distance traveled

Place an x on the ground where Marty is to start, this could be with tape or a pencil/pen mark on a piece of paper stuck to the ground.

After Marty walks a 'whole' distance, mark the stopping point and have a volunteer measure the distance to the nearest unit.

Replace the starting x with a green card so that the code will run without stopping and starting.

Mark to the side of Marty's path the fraction this distance represents. The first mark should be 1/2. Ask learners, without measuring, about how far it is to the half measurement: if the distance for the initial path was 30 cm / 12 in, the halfway point should be 15cm / 6 in.

It would be helpful to choose fractions that all for whole number quotients when dividing by the denominator: try to avoid odd number full distances as that will result in a fractional quotient.

Change the fraction to have Marty show the different fractional distances before placing them back on the green card. Maintain unit fractions for the demonstration.

Repeat the process of marking in the different fractions to indicate how far Marty has walked.

Share with learners the practice activity in the workbook, in the resources section, which shows several straight lines with Marty indicating about 1/2, 1/3, 1/4, 1/5. Learners need to mark the number line with different fractional distances, as indicated for each of the questions. Some questions include 1/2, 1/3, 1/4 and 1/5; if learners feel that including each of the unit fractions would support the task, encourage them to do so.

Bring learners back together to discuss if they found anything challenging about identifying how much a fraction is worth. 

How did you decide where to place each fraction on the number line?

Did you think of any interesting ways to check that your estimates were good?

Can you think of any times people use fractions for distances in the real world, like we did today?

Some tape to mark the floor, to compare fractions to a whole

Workbook for Fraction Number Lines

Determine Fractional Measurements using a Number Line

Mathematics - Middle Years - Lesson 2 - Using a Fraction Number Line

This pack has two lessons introducing fractions to learners. The first lesson introduces fractions as an equal part of a whole, with Marty demonstrating the differences in the length of a fraction. The second shows parts of a whole with a number line, where Marty walks several distances of different length but all relevant to a 'whole'. Learners will need to estimate about how far along a number line each fraction is

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Mathematics Lesson Pack - Middle Years - Fractions

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