Lesson

There are some great strategies for division , that we've used for smaller numbers, up to 3 digits long. How many can you remember?

Find 769\div3 by doing the following:

a

Find 600\div 3.

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b

Find 150\div3.

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c

Find 18\div3.

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d

Using the fact that 769=600+150+18+1, complete the statement with the missing numbers:

3 goes into seven hundred sixty nine ⬚ times with a remainder of ⬚.

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Idea summary

The part of a number that cannot be divided into equal groups is called the remainder.

Dividing by one number can often help us when we need to divide by a different number, as we see here.

Find the value of 40\div4.

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Idea summary

To make a division easier, we can divide both numbers by 2.

We can also think of dividing by 4 as dividing by 2 twice.

Dividing by other digits means we can use things like partitioning or the area model to help us.

Let's use an area model to find the answer to 133\div 7.

a

We set up the area model using a rectangle like this:

Now if we don't know straight away what 133\div 7 is, we start with something we do know, like groups of 10.

Find the area used so far if we take out 10 groups of 7.

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b

How much area is remaining?

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c

What is the width of the second rectangle?

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d

Using the area model above, what is 133\div7?

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Idea summary

Multiplication strategy | Division strategy | Example | Calculation |
---|---|---|---|

\text{repeated addition} | \text{repeated subtraction} | 32\div 8 | \text{subtract } 8 \text{ from } 32 \\\text{until we get to zero} |

\text{double-double} | \text{half-half} | 32\div 4 | \text{half of } 32, \text{ and then} \\\text{half of that} |

\text{partitioning} \\\text{by place value} | \text{partitioning} \\\text{by place value} | 230\div 5 | \text{split } 230 \text{ into } \\200+30,\\ \text{and divide each } \\\text{part by } 5 \text{ separately} |

\text{splitting number} | \text{splitting number} | 56\div8 | \text{split } 56 \text{ into } \\40+16,\\ \text{and divide each } \\\text{part by } 8 \text{ separately} |