The Take-Away Bar 1

Before introducing the learning object

1. Before introducing the students teachers need to find out if the students are ready for this learning activity.
2. Ask the students to work out a subtraction problem at this level silently. The following problem could be posed; "Tenna has $25, she gives $8 to her friend, how much does Tenna have left?" Observe the students as they solve the problem.
3. Note the students who find this problem easy or answer very quickly. These students may need to be given alternative work, as they already know how to easily work out subtraction problems. These students are ready to work independently of the teacher using the learning object and will likely need to progress through this unit a lot quicker than others. The Level 3 version of this learning object is suitable for more able students.
4. 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.

Introduction to 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 take-away bar: generate easy subtractions" version of the learning object for this introduction.
2. Click "Go".
3. Click "Solve".
4. Click on the arrow several times to see what the learning object does, reading out and work through the instructions in Tenna’s speech bubbles.
   
5. Place the cursor over the slider, click and hold, to move it.
6. Move the slider to 7. Ask the students why this might be helpful.
7. Continue solving the problem by working out the remaining part to be subtracted. Then work out the answer and type it in the box.
8. At the same time as working with the learning object it is recommended that the teacher draws an open number line showing the steps in the strategy to assist the student’s understanding. For example;
   
9. The open number line is also a good way to show students what needs to be worked out.
   
10. Click on "Reset" to start the same problem again. This time initially move the slider to another number. Work through this process several times reminding the students that this strategy is about breaking the number into parts and subtracting the number part by part. The fact that the number being subtracted can be broken up into different parts and they will all lead to the correct answer is important in understanding this strategy.
    
11. This learning object will allow students to subtract the 8 in 17 – 8 = one at a time. This is to be discouraged as this is stage 4 thinking, a counting strategy.
    
12. The deciding which part to subtract first is central to understanding this strategy. The goal is for students to automatically see and know the benefit of initially subtracting 5 from 15 in 15 – 8 =, or subtracting 3 from 23 in 23 – 8 =, or 6 from 46 in 46 – 7 =. Student may initially subtract a variety of numbers and not necessarily the most efficient number. At this stage the focus is on subtracting the number part by part, with working out the most efficient parts to subtract is the focus of stage 6.
13. The following is one way to subtraction 8 from 17 part by part. In this case 2 was subtracted first, then 5, and then 1. This is an acceptable way to solve this problem at this stage.
     
    
    
14. Click on "Reset" to start the problem one more time. This time suggest that first subtracting 10 may be another way to solve the problem without counting. Ask the students how subtracting 10 first might make it easy to work out 17 – 8 =. Show the students subtracting 10 using the learning object. A hint will appear to help the students, "You have taken away an extra amount. Remember to add it back on!"
     
    
    
15. Away from the computer, organize the students into pairs and get them to prepare a presentation on how "The Take-Away Bar" learning object works and why it makes answering subtraction problems 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?
    • Why would 6 be a good number to first move the slider to in 26 - 9?
    • What number would not be good to use? Why?
    • Would you move it past 9? Why?
16. At this stage most students will be ready to move on to working independently of the teacher. Before this check they can move the slider, and understand when to use the "Hint", "Help", "Reset" and "New Equation" buttons.
17. The teacher needs to keep working through a couple more examples with students who are not ready to work independently before leaving all students to work with the learning object themselves.

Students working independently with the learning object

1. Once the students have started to gain confidence in solving subtraction 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 explain their thinking.
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 the 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?
   • What was the first number you took away? Why?
   • Was this easier than counting back?
   • How did breaking up the number make it easier?
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. Explaining the number line to another student is also an excellent way of developing understanding.
6. As students become confident at solving the subtraction problems, they can be challenged to solve a problem by thinking about and imaging the learning object but not actually touching the learning object. The goal is to get students to the point when they can quickly and easily solve subtraction problems in their heads. The learning object is a tool to help students develop this ability, a means to an end.
7. The other version of "The Take-Away Bar" can also be used. This version allows students or teachers to make up their own difference problems. At this level any single digit number and any two-digit number can be typed in to make a subtraction problem.
   Click here: The take-away bar: make your own easy subtractions
   
8. Students who find the problems at this level too easy can moved on to "The Take-Away Bar" - Level 3 learning object.