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# 2.15 Division: partitioning leading to short division

Created on 01 August 2019 by ncetm_administrator
Updated on 01 August 2019 by ncetm_administrator

## Introduction

Introduce the short division algorithm, using it to divide two-/three-digit numbers by single-digit numbers; explore exchange where necessary.

## Teaching points

• Teaching point 1: Any two-digit number can be divided by a single-digit number, by partitioning the two-digit number into tens and ones, dividing the parts by the single-digit number, then adding the partial quotients; if dividing the tens gives a remainder of one or more tens, we must exchange the remaining tens for ones before dividing the resulting ones value by the single-digit number.

• Teaching point 2: Any two-digit number can be divided by a single-digit number using an algorithm called ‘short division’; the algorithm is applied working from the most significant digit (on the left) to the least significant digit (on the right); if there is a remainder in the tens column, we must ‘exchange’.

• Teaching point 3: Any three-digit number can be divided by a single-digit number, by partitioning the two-digit number into hundreds, tens and ones, dividing the parts by the single-digit number, then adding the partial quotients; if dividing the hundreds gives a remainder of one or more hundreds, we must exchange the remaining hundreds for tens before dividing the resulting tens value by the single-digit number.

• Teaching point 4: Any three-digit number can be divided by a single-digit number using the short-division algorithm.

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## Comments

10 February 2020 15:57
Yes you are correct we are using the sharing (partitive structure) for division, so 7 tens distributed between 3 is 2 tens each with one group of ten remaining - this cannot be distributed equally as one ten and needs to be renamed as 10 ones
 By Debbie_Morgan Alert us about this comment
09 February 2020 15:04
I found the language and images used in this section could a little confusing. It seems that the language of sharing is used. e,g, 7 tens divided by 3 is 2 tens remainder 1 ten but the image of the place value counters is showing the tens being grouped. Should it be 7 tens divided by 3 tens is 2 remainder 1 ten? Or should the image be different?
 By leah_edmunds Alert us about this comment
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