Minds On

Equal teams

At recess, the Grade 4 students from all classes wanted to play a game. There were 68 students in all. How will we create 2 equal teams? How many students will be on each team?

Brainstorm

Representing our thinking

What strategies could you use to divide the 68 students into 2 teams and find out how many will be on each team?

In your notebook or another method, try to use objects, images, numbers, diagrams or words to show how you would divide the students?

Action

How many players on the team?

There are 68 Grade 4 students in total, and we need to divide them into 2 teams.
How many students will be on each team?

The math statement for our soccer team situation is 68 divided by 2, or in symbols:

68 ÷ 2 = ?

We can also represent this equation as a fraction. Access the following episode of Homework Zone, where Teacher Troy demonstrates how a fraction is another way to express division.

In fraction form, 68 divided by 2 would have 68 as the numerator and 2 as the denominator.

68 divided by 2 is represented in fraction form with 68 labelled as the numerator and 2 labelled as the denominator.

Exploring division strategies

Let’s explore some strategies that we could use to solve this question.

Using an array

Using cubes, counters, objects or shapes, we can take 68 pieces and arrange them into 2 rows. Next, we can count how many pieces are in each row to know how many students will be on each team.

Two groupings of 34 squares, each organized in a single line.

Decomposing numbers

The number 68 is represented by 6 tens and 8 ones. Decomposing the number, or expressing 68 in expanded form, we have 60 + 8 = 68.

Expanded form often gives us “friendlier numbers”. Friendlier numbers are numbers that are easier to work with.

We can use the expanded form and the friendlier numbers 60 and 8 to divide each number separately.

A diagram shows the number 68 in expanded form. On the left side, there are sixty purple circles divided into two clusters of thirty, and on the right side, eight purple circles are divided into two clusters of four. Thirty pieces plus four pieces equals 34 pieces in each group

Using long division

We can also express and solve 68 ÷ 2 using long division. Examine the following image to learn more about the long division format.

68 divided by two is represented in long division form. Two is labelled as the divisor, 68 is labelled as the dividend, and there is a question mark labelled as the quotient.

Let’s examine the steps to long division.

The steps for dividing 68 by two in long division are as follows: first figure out how many times 2 goes into 6, and add that number (3) above the 6. Then multiply the 3 by the divisor (2), and add the product (6) below the 6 in 68. Subtract 6 from the 6 in 68 and add a zero below the second 6. Next, figure out how many times the divisor (2) goes into 8, and add that number (4) above the 8 to the left of the 3. Multiply the 4 by the divisor (2), and add that product (8) below the 8 in 68. Subtract the 8 from the 8. When you reach zero, the division is complete.

Since 68 ÷ 2 = 34, each team will have 34 students.

Test your skill

Test Your Skills

Choose your strategy

In your notebook or using a method of your choice, create an equation for this scenario and solve it using a strategy of your choice.

  • A farmer has 92 apples that need to be divided evenly between 4 baskets. How many apples will there be in each basket?

When you’re ready, press 'Solution' to access the answer.

92 ÷ 4 = 23

Dealing with remainders

What if one more student arrived and wanted to play soccer too? With 69 students, could we create two teams with an equal number of players?

Let’s examine the long division.

So, each team would have 34 players on it, but there would be one extra student leftover.

When we have a leftover amount that cannot be divided any further, we call this a remainder. In our math equation we express a remainder like this:

69 ÷ 2 = 34 R1

This means that we cannot create 2 equal teams because there will be one remaining student. So, one team will need to have an extra player!

Practice

Imagine that your school is 1 of 3 neighbourhood schools participating in a local Environment Day. Your city or town is providing a total of 545 saplings (baby trees) for the 3 schools to plant in a nearby ravine. How many trees does each school get to plant?

In your notebook or using a method of your choice, create an equation for this scenario and solve it using a strategy of your choice.

How many trees will each school receive?

When you’re ready, press 'Sample Answer' to access a solution using long division.

The steps for dividing 545 by three are as follows: first, see how many times 3 goes into five and add that number (1) above the line above the first 5. Multiply that number by 5 and add the product (3) below the first five, then subtract five minus three. The remainder (2) goes below the three. Then see how many times the divisor (3) goes into 2 - since 3 is larger than 2, borrow the 4 in the above line and place it beside the remainder 2, creating the number 24. Now add the number of times that 3 goes into 24 (which is 8) above the line beside the 1. Now multiply that 3 by the divisor again (3) and add the product (24) below the first 24. Subtract 24 from 24, and add a line with a zero below. Borrow the remaining 5 in 545 and place it to the right of the zero, and then see how many times the divisor (3) goes into 5, which is just once. Add 1 above the 5 above the dividing line, and multiple 1 by 3, adding 3 below the 5 at the very bottom. Subtract three from five, and add the remainder beside the expression at the top as "R2".

In the tree planting scenario, what does the remainder of 2 mean or represent? Record your thinking in a notebook or using a method of your choice.

Consolidation

Practice

Choose 1 of the following questions and create a math statement independently:

  • If each student in your class of 28 students make groups of 3 to plant trees, how many groups of exactly 3 students can be formed?
  • If each student in your class of 28 students make groups of 4, how many groups of exactly 4 students will there be?
  • If each student in your class of 28 students make groups of 5, how many groups of exactly 4 students will there be?

Express the math statement using the long division format. Calculate the quotient.

Express the final answer to include the remainder as a fraction form as well as the remainder using “R” with the remainder value as in the example 181 R2.

Demonstrate and/or explain your work and final answer.

Reflection

As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.

I feel...

Now, record your ideas using a voice recorder, speech-to-text, or writing tool.

Press 'Discover More' to extend your skills.

There are 257 students at Autumn Public School. It is a brand-new Eco school with a focus on environmental issues. Their classes have more than one grade together. There are only 9 classrooms. How many students should be in each class?

If there is a remainder value, express the final answer to include the remainder as a fraction form, and the remainder using “R” with the remainder value.

Show and/or explain your work and final answer.

Can there be an equal number of students in each class? Explain your answer.