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Number (mult/div)
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Grade 5

EXT: Area or array model - divide a 4 digit number by a 1 digit number

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Lesson

When we need to divide a four digit number, such as 4000 by a one digit number, such as 8, we can use arrays and area models to help us.   We can also start with a simpler problem, such as 40 divided by 8, and then think about how this helps us with our final answer.

Worked examples

Question 1

Let's use an area model to find the answer to $8024\div8$8024÷​8.

  1. We set up the area model using a rectangle like this.

    $8$8
    Total area: $8024$8024

    Now if we don't know straight away what $8024\div8$8024÷​8 is, we start with something we do know, like groups of $1000$1000.

    Fill in the area used so far if we take out $1000$1000 groups of $8$8.

    $1000$1000
    $8$8 $\editable{}$
    Total area: $8024$8024

  2. How much area is remaining?

    $1000$1000
    $8$8 $8000$8000 $\editable{}$
    Total area: $8024$8024

  3. What is the width of the second rectangle?

      $1000$1000 $\editable{}$
    $8$8 $8000$8000 $24$24
      Total area: $8024$8024

  4. Using the area model above, what is $8024\div8$8024÷​8?

Question 2

We want to find $8104\div8$8104÷​8.

  1. Fill in the boxes to complete the area model.

      $1000$1000 $10$10 $\editable{}$
    $8$8 $\editable{}$ $\editable{}$ $\editable{}$
      Total area: $8104$8104

  2. Using the area model above, what is $8104\div8$8104÷​8?

Question 3

We want to find $4045\div5$4045÷​5.

  1. Fill in the widths of the rectangles on the area model.

    $\editable{}$ $\editable{}$
    $5$5 $4000$4000 $45$45
    Total area: $4045$4045

  2. Using the area model above, what is $4045\div5$4045÷​5?

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