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

45 Minutes

Lesson Overview

This lesson is about comparing fractions within the same whole. How far 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.

Key vocabulary:
    fraction, half, third, quarter/fourth, fifth,

Content Sections

  • Learning Objectives
  • Pre-Lesson Preparation
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  • Warm-Up
  • Get Learning
  • Time for Practice
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    • Cool Down
      • Extensions & Challenges
      • Extend
      • Support
      • Additional Reading
      • Mathematics - Middle Years - Lesson 2 - Using a Fraction Number Line

        45 Minutes

        Lesson Overview

        This lesson is about comparing fractions within the same whole. How far 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.

        Key vocabulary:
          fraction, half, third, quarter/fourth, fifth,
        • Fractions of a whole
        • Tablet with Bluetooth 4.2+
        • Mathematics - Fractions
          • Activity pages
          • Marty the Robot V2
          • A device with MartyBlocks to show the fraction lengths in action
          • Some tape to mark the floor, to compare fractions to a whole

        Learning Objectives

        • I can compare fractions on a number line​.
        • I can compare unit and other proper fractions.

        Pre-Lesson Preparation

        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.

        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.

        Warm-Up

        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

        Below is the procedure for the game

        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.

        Get Learning

        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.

        Time for Practice

        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.

        Cool Down

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

        Suggested questions you might ask:

        • 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?

        Carry out any end of lesson routines.

        Extensions & Support

        Extend

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

        Support

        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.

        Additional Reading

        Connecting with MartyBlocks


        • CSTA Education Standards
        • National Curriculum - Mathematics KS2: Number - fractions
        • Mathematics:
        • Literacy & English: Listening and Talking
        • Health and Wellbeing: Mental, Emotional, Social and Physical Wellbeing
        • Numeracy: Number, Money and Measure
        • Australian Curriculum - Mathematics: Number and Algebra - Fractions and decimals
        • Elementary Math: Knowledge and Skills