# Mathematical reasoning

Hi Year 6,

We are nearly at the end of our journey at Broad Heath. You have made great improvements in your problem solving and reasoning since the start of the year; you have worked hard to develop these skills in class, on the blog and at home.

Problem Solving and reasoning will continue to be a great challenge for next year’s Year 5 classes and also for you all when you move on to secondary school. Here’s one last push – please watch the fantastic video below and use the information to help you write a clear, well reasoned explanation about how to use the short method for division. Choose your own question and explain it in a post below (remembering to not  miss out any steps and demonstrate excellent vocabulary and understanding of Place Value).

## 3 thoughts on “Mathematical reasoning”

1. Ryan Chand

First step is to set out the bus stop method and write the divisor and number. Secondly, you need to see how many 3’s go into 3, which is 1 so you need to write that above the number 3 (3612).Thirdly, you need to see how many 6’s go into 3, which is 2 so you need to write that above the number 6 (3612). Fourthly, you need to see how many 1’s go into 1 you can’t do that so you need to carry that 1 and write it next to the 2. This makes it easier and we now know how many 3’s goes into 12, which equals 4. We need to write the 4 above the 1 and the 2.
3612/3=124.

2. Anthony Dacosta-Reid

To write the problem correctly, place the divisor, the number that you’re dividing into another number, outside the short division bar. Place the dividend, the number that you’ll be dividing by the divisor, inside the long division bar. The result, will go on top of the division bar. Remember that for short division to work, your divisor has to be less than 10.
For example: In 847/5, 5 is the divisor, so write it outside the division bar. 847 is the dividend, so place it inside the division bar.

When you divide, you are stating how many times one number can fit into another number. For example, 2 can fit into 6 three times (2 + 2 + 2 =6). Continuing with our example, 5 goes into 8 just one time, but it doesn’t evenly divide into 8. We have 3 left over. Write the number 1, the first number of the quotient, on top of the division bar. This leftover number is called the remainder.
If you were using long division, you would write out 8 minus 5 equals 3 and then bring down the 4 from the dividend. Short division simplifies this written process.

Write the remainder next to the first number of the dividend. Write a small 3 to the top right of the number 8. This will remind you that there was a remainder of 3 when you divided 8 by 5. The next number you will divide into is the combination of the remainder and the second number.
In my example, the next number is 34.

Divide the number formed by the first remainder and the second number in the dividend by the divisor. The remainder is 3 and the second number of the dividend is 4, so the new number you’ll be working with is 34.
Now, divide 34 by 5. 5 goes into 34 six times (5 x 6 =30) with a remainder of 4.
Write your result, 6, on the division bar to the right of the 1.

Write the second remainder above the second number in the dividend and divide. Just as you did the first time, simply write a small 4 above and to the right of the number 4. The next number you will be dividing by is 47.
Now, divide 47 by 5. 5 goes into 47 nine times (5 x 9 = 45) with a remainder of 2.
Write your answer, 9, on the division bar to the right of the 6.

Write the final remainder on the division bar. Write “r 2” to the right of the result on the division bar. The final answer of 847/5 is 169 with a remainder 2.

3. Plaiza Karan

I will do it over the weekend and give it to Mr McCabe on Monday. 😇