The Difference Bar 2

Introduction to the learning object

1. This unit is the same as the Level 2 learning object The Difference Bar 1 except the numbers used are larger. Level 2 is about finding the difference between numbers where the difference is less than 10. Level 3 is about finding the difference between any 2 two-digit numbers.
2. This unit assumes students already know how to use this learning object. If not the Level 2 unit gives suggestions how to introduce students to this learning object. Features of the introduction are; understanding the idea of difference, its use in life and making sure students are at the appropriate stage of development. The The Difference Bar 1 Level 2 unit is available.

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: make your own hard 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 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. 10. 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. 20 more. Ask the students if they can work out how this might make it easier to work out.
   
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;
    • Explain why you do that?
    • How does breaking up the numbers help work out the difference?
    • What number would not be good to use? Why?
    • Why is it sometimes good to move the slider past the end?
    • 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

The 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 35 long and the blue strip represents a strip 17 long. The blue 17 strip is placed on top of the yellow 35 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.
   
2. Moving the slider to the right breaks the difference into two parts. Breaking up the difference can be used to help work out its length. As the slider is moved, the distance moved is shown underneath the strip.
   
3. A way to view this is to think;
   "17 plus the difference equals 35"
   or 17 + D = 35 (where D is shorthand for difference)
   By breaking up the difference to be ‘3 and something’ we are now saying that;
   "17 plus 3 plus something equals 35"
   or 17 + 3 + S = 35 (where S is shorthand for some number)
   or 20 + S = 35
   
4. Moving the slider again breaks up the remaining part of the difference. We know the yellow length is 35, number at the top, and the blue is 17, one part of the difference is 3, another part is 10 and one part is left.
   17 + 3 + 10 + P = 35, (where P is shorthand for the part that is left)
   20 + 10 + P = 35
   30 + P = 35
   
5. Reminding ourselves what we are trying to work out, i.e. the difference, we can work out that the last part is 5.
   
   Another way to model this for students is with a number line.
   
6. Click "Reset" to start the problem again. This time move the slider to 20 and ask the students to explain how to work out the difference this time.

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 leading 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 to understand this strategy is to get them to draw a diagram showing their thinking. 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 allowing students or teachers to make up their own difference problems. At this level any two-digit numbers can be inserted to find the difference. Click here: The difference bar: make your own hard subtractions