The Difference Bar 1

Introduction to the learning object

1. Start by asking the students to think of situations when you might want to find the difference between two numbers. This is before introducing the learning object on the computer.
2. The following examples may be mentioned. If not, the teacher can introduce them to the students:
   • working out how much taller someone is compared to another person;
   • finding the difference between the distance you can kick a ball with the distance your teacher can kick a ball;
   • seeing how many more dollars need to be saved before something can be purchased, e.g. $15 saved, the toy costs $23, how much more to save?
   • working out how far to travel on a trip, e.g. A trip is 16 km, you have traveled 9 km, how far to go?
3. Ask the students to work out a difference problem silently. Use one of the examples above, a student’s problem or simply ask, What is the difference between 16 and 22? Observe the students as they solve the problem.
4. Note the students who find the problem easy or answer very quickly. These students may need to be given alternative work, as they already know how to work out differences or they need to progress through this unit a lot quicker than others or be given harder examples. The Level 3 version of this learning object is suitable for more able students.
5. Also note students who use a counting method or struggle to solve the problem. If a counting method is used the student needs to be asked if they can work out the problem without counting, i.e. use another strategy. If a student cannot solve the problem or only uses a counting strategy, then this unit may not be suitable for them.

Working with the learning object

1. With a group of students the teacher demonstrates the learning object by working through a problem, explaining and showing the students what to do. Use The difference bar: generate easy subtractions version of the learning object for this introduction.
2. Click "Go".
3. Click "Solve".
4. Click on the right arrow several times to see what the learning object does. Then read out and work through the instructions in Dario's speech bubbles.
   
5. Place the cursor over the triangle, click and hold, then move the slider.
6. Move the slider to 3. Ask the students why this might be helpful.
7. Continue solving the problem by working out the remaining part of the difference then combining the two parts to find the difference.
8. Click on "Reset" to start the same problem again. This time initially move the slider to another number, e.g. 1. Work through the process again, reminding the students that we are looking for numbers that will make it easy to work out without any counting. This step is to show the students that the slider can be moved to many numbers. Solve the problem again.
9. Click on "Reset" to start the problem one more time. This time initially move the slider past the end, e.g. 10. Ask this students if they can work out how this might make it easier to work out. The learning object gives hints to help the student work out what to do. In this case, "You have added an extra amount. Remember to take it away!"
   
10. Away from the computer, organize the students into pairs and get them to prepare a presentation on how "The Difference Bar" learning object works and why it makes working differences out easier. As the pairs are preparing, the teacher needs to observe and listen, to work out the level of support each pair of students needs as they move to working with the learning object on their own. The following questions could be used to help determine the students understanding;
    • Why do that?
    • How does breaking up the numbers help work out the difference?
    • Why is 3 a good number to move the slider to?
    • What number would not be good to use? Why?
    • How could you check you have the correct answer before the computer tells you?
11. At this stage most students will be ready to move on to working independently of the teacher. Before the work independently check they can move the slider, and understand when to use the "Hint", "Help", "Reset" and "New Equation" buttons.

Step by step guide to working with the learning object

Following is a step by step guide to solving one difference problem using the learning object. Most students will not need to be given this, as they will intuitively know what to do or quickly learn by using the learning object. The following can be used with the few students who need it or used by teachers seeking a more detailed understanding of the learning object.

1. The yellow strip in the learning object represents a length 25 long and the blue strip represents a strip 17 long. The blue 17 strip is placed on top of the yellow 25 strip and their ends lined up at the left. The yellow on the right that is not covered by the blue is the difference between their lengths. This length, the difference, is what students are trying to work out. This can be modeled using strips of card or paper if the students are having trouble understanding the concept of difference.
   
   Another way to describe difference is to imagine two people throwing a ball. They both throw from the cone on the left. The first person throws a distance of 17, a cone is placed 17 from the start. The second person throws a distance of 25 and a second cone is placed 25 from the start. The difference is the distance between how far the two people threw.
   
2. Using the learning object on the computer moving the slider to the right breaks the difference into two parts. Breaking up the difference into parts will be used to work out its length. As the slider is moved, the distance moved is shown underneath the strip. The idea is to move the slider to get a number that will help. In this problem the slider is moved 3 to the right. The slider could be moved 1, 2, 3, 4, 5, 6, 7 or even past the end of the strips, but moving it 3 will make it easier to work out the difference, see below. Use Dario’s speech bubble comments to work out what to do next.
   
3. One way to view what we are doing is to think;
   "17 plus the difference equals 25"
   By breaking up the difference to be ‘3 and something’ we are now saying that;
   "17 plus 3 plus something equals 25"
   or "20 plus something equals 25"
4. This next screen appears after filling in the white box alongside "What number are you up to? Hint: 17 + 3 =" and pushing enter or return.
   
5. We know the whole length is 25, number at the top, and the blue is 17, the yellow (one part of the difference) is 3 and the remaining part of the difference is 5. If the 5 was not shown we could still work out it’s length because 17 + 3 = 20 and 20 + 5 = 25.
6. Reminding ourselves what we are trying to work out, i.e. the difference, we can see that the difference is 3 and 5, which equals 8. The difference is 8. 17 + 8 = 25
   Another way to model this for students is with a number line.
   
7. To confirm the students understand this strategy ask them some of the following questions;
   • Why was the slider moved to 3?
   • Why not move it to 5?
   • What other numbers you could use to make it easier to work out?
   This strategy of adding a number so the answer is a multiple of 10 is called rounding to the nearest 10 or using a tidy number.
8. Click "Reset" to start the problem again. This time move the slider past the end of the strip to 10 and ask the students to tell you how to work out the difference this time. This strategy is called compensation.
   
   
   

Students working independently with the learning object

1. Once the student has started to gain confidence in solving difference problems using the learning object, leave them to work on their own. Two students working together on the one computer is best as it allows the students to talk through their thinking, which is to be encouraged. Make sure each student has a turn controlling and using the keyboard as well as lead the problem solving and having to explain their thinking as they do it.
2. The teacher’s role now changes to one of observer and helper. The learning object generates all the problems to be solved. This allows the teacher time to watch and listen to students so they can identify any misunderstandings or pieces of knowledge causing problems for individual students.
3. At times the recall of knowledge, e.g. basic facts, causes students to have difficulty solving problems. Teachers need to be vigilant for knowledge difficulties and give the student specific work to address any problems when identified.
4. As the teacher moves around, the following questions could be used to draw out the students thinking:
   • How did you use the learning object to solve the problem?
   • What strategy did you use?
   • Why did you break up the numbers as you did?
   • How did breaking up the number make it easier?
   • What would have been a way of breaking up the number that would not have made it easier?
   • Would the strategy "round to the nearest 10" or "compensation" be the best strategy with these numbers? Why? (The "Hint" button has explanations of these strategies)
5. A way to assist students understand this part-whole thinking is to get them to draw a diagram showing their strategy. Using a number line like the ones above would be one way to represent their thinking but other methods to record their thinking is also to be encouraged. Explaining the number line to another student is also an excellent way of developing understanding.
6. As students become confident at solving the difference problems, they can be challenged to solve a problem by thinking about and imaging the learning object but not actually touching the learning object.
7. The other version of "The Difference Bar" can also be used. This version allows students or teachers to make up their own difference problems. At this level a single digit number and a two-digit number can be inserted to find the difference. Click here: The difference bar: make your own easy subtractions
8. Students who find the difference problems too easy can be moved on to "The Difference Bar" - Level 3 learning object. At this level the difference between any 2 two-digit numbers need to be solved.