The divider (whole number remainders)

Working with the learning object with students

Teaching session 1

In this teaching session the students use the learning object to solve problems where the quotient is a whole number. We suggest that you use the Divider: solve your own problem however you could use the Divider: without remainders, which generates problems randomly.

1. Show students the Divider and introduce them to David. Explain that the purpose of the learning object is to solve division problems by splitting them into easier to solve parts.
2. Enter a problem into the learning object, for example: 45 ÷ 5
3. Discuss what the numbers on the bar represent.
   Why do you think that 45 is written in the bar?
   What does the 5 on the side of the bar represent?
4. Show that the bar represents 45 and that five is the length of the side. The length of the top side is what they are trying to solve. You may also like to represent the problem as 5 x ? = 45
5. Ask the students if any know the answer to the problem. If all the students know the answer show them where to enter it and how their response is checked. Select a new problem - this time choosing one where the problem is not a known fact.
6. If at least some of the students did not know the answer to the problem show the students how to split the bar into parts. Each of these parts is represented by a division which is shown in the boxes above the bar. Tell the students that the aim is to split the bar until they see a division that they know the answer to. For example split the bar into 25 (25 ÷ 5) and 20 (20 ÷ 5).
   
7. Show how to enter the answer into the first box (25 ÷ 5 = 5). Point out how this number appears along the bottom of the bar and also that it is entered in the equation at the foot of the learning object screen.
   What does this [pointing to 5] represent?
   Where is this number in the equation? Why is it there?
8. Ask if they know the answer to the second box.
9. If they do, enter the answer (20 ÷ 5= 4). If not show how 20 can be split into smaller parts.
10. Discuss how the final answer requires them to sum the numbers along the bottom of the bar and show how this is represented in the equation.
    What is the answer to 45 ÷ 5 ?
    How did we work it out?
    Why did we do it that way??
    Could we have done it another way? If another way is suggested then click Reset and complete the problem again using different parts/splits.
11. Repeat with other division problems where the quotient is a whole number. We suggest that the problems are also posed in context so that the students are required to think which numbers from the problem need to be entered into the learning object. Possible problems include: Samantha has gathered 84 eggs to sell at the Farmers market. She wants to put them into cartons of six. How many cartons can she fill? 126 people came to the netball trials. How many teams of seven players can be made for the trials?

Teaching Session 2

In this teaching session the students use the learning object to solve problems where there is a remainder. In this case the remainder is left as a whole number. For this session use the Divider: with whole number remainders , which generates problems randomly. Note that not all problems presented have remainders as the problems are generated randomly.

1. Ask the students to remind you why the Divider is helpful for solving division problems. Reinforce the idea that the divider allows you to split up division problems into parts that you already know the answer to.
   How does the divider help you solve division problems?
2. Check that the problem posed has a remainder. If it doesn't select a new problem until you are presented with a problem that has a remainder. Click solve.
3. Check that the students know what the numbers on the bar represent. Why do you think that [dividend] is written in the bar? Why is [divisor] written on the side?
4. Ask students to suggest where the problem could first be split. Split the bar and record the answer. For example:
   
5. Direct the students attention to the remaining part which in this example is 14 ÷ 6. Do you know 14 ÷ 6? Discuss that this problem does not have a whole number answer.
6. Move the bars to show 12 ÷ 6. Illustrate the use of the + - arrow to move the slider in ones. Enter the answer in the box.
   
7. Discuss the remainder 2 in the final bar.
8. Discuss how the final answer requires them to sum the numbers along the bottom of the bar and show how this is represented in the equation. Show that the remainder is expressed in the answer as r 2.
   What is the answer to 74 ÷ 6?
   How did we work it out?
   Why did we do it that way?
   Could we have done it another way? If another way is suggested then click Reset and complete the problem again using different parts/splits.
9. Repeat with other division problems where there is a remainder. We suggest that the problems are also posed in context so that the students are required to think which numbers from the problem need to be entered into the learning object. Possible problems include:
   Samantha has gathered 86 eggs to sell at the Farmers market. She wants to put them into cartons of six. How many cartons can she fill?
   69 people came to the sevens rugby trials. How many teams of seven players can be made for the trials?
   Crepes are sold in packs of 5 from the Farmers market. How many packs can be made from the 73 crepes made?

Students working independently with the Divider learning objects (no remainders)

Pose problems set in context for the students to solve independently (individually or in pairs) using the Divider: solve your own problem learning object. Alternatively direct the students to use the Divider: without remainders, learning object and ask them to create contexts for the problems generated.

Possible contexts for division problems:

Paving stones

Joe is paving the path. The path is 4 paving stones wide. How many rows can he tile if he has 64 paving stones.

Packing

Tash is packing biscuits into trays for the school fair. She can fit 8 biscuits on a tray. How many trays can she fill with 136 biscuits?

Once students have solved the problem encourage them to make a written record of the way that they solved the problem. For example the students may record the ways that they split the division problem into parts.

136 ÷ 8 = 17

Alternatively students can print the solution screen within the learning object. Provide opportunities to share solution strategies and written records with others.

How did you use the divider to solve the problem?
What numbers did you use? Why did you use these numbers?
How did you record your thinking?

Students working independently with the Divider learning object: whole number remainders

If you want the students to solve problems with whole number remainders you need to use the Divider: whole number remainder learning object as The Divider: solve your own problem learning object supports fractional answers.

Encourage the students to create a context for the division problem that they solve. Once students have solved the problem encourage them to make a written record of the way that they solved the problem. For example the students may record the ways that they split the division problem into parts.

Luke collected 139 eggs to sell at the farmers market. He put them into 23 cartons of 6 eggs and had one left over.

139 ÷ 6 = 23 r 1

Alternatively students can print the solution screen within the learning object. Provide opportunities to share solution strategies and written records with others.

How did you use the divider to solve the problem?
What numbers did you use? Why did you use these numbers?
How did you record your thinking?

Students working independently without the learning object

Independent activities that develop the same concepts as the learning object include:

• Figure It Out, Number Sense and Algebraic Thinking, Book 1, Level 3, page 8, Just Right
• Figure It Out, Number, Book 3, Level 3, page 18, Arcade Adventure
• Figure It Out, Number, Book 3, Level 3, page 19, Wheels Galore
• Figure It Out, Number, Book 2, Level 3, page 15, Sweet Thoughts

Students could also work independently on division problems:

• Pose the students division problems (with and without remainders) in context to solve. Encourage them to make a written record of the way that they solved the problem. For example the students may record the ways that they split the division problem into parts (see above).
• Pose the students division problems as equations. First ask the students to create a context for the equations. Encourage them to make a written record of the way that they solved the problem. For example the students may record the ways that they split the division problem into parts (see above) or write a list of the splits.

Provide opportunities to share solution strategies and written records with others.

How did you use the divider to solve the problem?
What numbers did you use? Why did you use these numbers?
How did you record your thinking? How does that help you solve the problem?