Video: Repeated addition of unit fractions

﻿Hello everyone, my name is Mrs. Darlene and I'll be teaching you your math lesson today. It's lesson number 13 on fractions. First of all, let's go through the practise activity that you had at the end of the last session. You were asked, Can you show you this fraction using a number line, and what will the written fraction be? Well, looking at the arrows, I see that there are eight arrows and seven of them are shaded. So my number line is going to be split into eight equal parts. Now to show the number of arrows that are shaded, my arrow is going to be pointing at seven-eighths, and the written fraction will be seven-eighths. Well done if you've got this at home. Let's go through the other practise activity that you had. Remember these panes of glass in the window, and some of the panes of glass were broken. The first thing you had to do was show the fraction of panes of glass that were broken on a number line and to write the written fraction too. Well, there are nine panes of glass in total. So your number line should have been split into nine equal parts. And to show the number of panes of glass that are broken, your arrow should have been pointing to four-ninths, and the written fraction is four-ninths. Now, if you had to go the extra bit that you had to do, you are asked, What fraction of the window pane did not break? Well, the number line will look same but this time, the arrow would be pointing to five-ninths, because five of the window panes were not broken and you would write this as five-ninths. Well done at home if you manage to draw both of those number lines and have the arrows pointing at the correct place on the number line and write the correct fraction as well. Have a look at this bar model. What is the unit fraction? Well, the bar model has been divided into five equal parts. So the unit fraction is one-fifth. How many one-fifth of it in three-fifths? Let's use this stem sentence to help us answer. There are three one-fifths in three-fifths. Have a go at saying that at home with me. There are three one-fifths in three-fifths, well done. I'm going to write an equation to show that if I have one-fifth, and another one-fifth, and another one-fifth, then I have three one-fifths, have a look. One-fifth add another one-fifth add another one-fifth equal three-fifths. There is another way that I can write this equation. Three-fifths equals one-fifth, add another one-fifth, add another one-fifth. Now let's look at this on a number line. My number line has been divided into five equal parts. I'm going to count up in fifths starting at zero. Zero, one-fifth, add another one-fifth, add another one-fifth, all together, I have three-fifths. One-fifth, add one-fifth, add one-fifth equals three-fifths. There is another way you can write this equation. Three fifths equals one-fifth, add one-fifth, add one-fifth. Let's have a go using a different shape and a different number line. First of all, what is our unit fraction? Well, my shape of my number line have been divided into nine equal parts. So my unit fraction is one-ninth. Now let's count up in ninths to work out how much of this shape has been shaded. One-ninth, and another one-ninth, and another one-ninth, and another one-ninth, make four-ninths. How can we write this using repeated addition of the unit fraction? Well, one-ninth, add one-ninth, add one-ninth, add one-ninth equals four-ninths. There's another way of writing this as an equation. Four-ninths equals one-ninth, add one-ninth, add one-ninth, add one-ninth. Let's have a go using our eggs and our egg boxes. First of all, what's the unit fraction? Well, the egg box and the number line have been divided into 12 equal parts. So our unit fraction is one-12th. Let's count up in 12ths. Remember to start at zero. Zero, one-12th, two-12ths, three-12ths, four-12ths, five-12ths, we have five-12ths. How would I write this using repeated addition of the unit fraction? Well, one-12th, add one-12th, add one-12th, add one-12th, add one-12th equals five-12ths. There's another way that you can write this equation. Five-12ths equals one-12th, add one-12th, add one-12th, add one-12th, add one-12th. Well done if you are following along with that at home. Your first practise activity for this session is, What repeated addition equation matches this number line? Let's have a look. So you've got some jumps on the number line, what addition equation matches this number line? You might want to draw out this number line and the jumps, making it so that each jump on the number line is one centimetre wide and using a ruler, I'll help you draw the number line. You can then write above each jump what has been added each time and then how much you have all together. Can you write the two different ways there are of making a repeated addition equation based on this number line. Your next practise activity is this, you have to work out whether this equation is true or false. Let's have a look at it. One-sixth, add one-sixth equals two-12ths. Can you draw a number line to represent this equation? What do you notice? Can you explain your answer? Use the number line to help you explain your answer. I hope you have fun doing that at home and I will see you soon.

Lesson summary: Repeated addition of unit fractions

In this lesson, we begin to write repeated addition equations to represent non-unit fractions.

Maths

Y4 Maths

Key Stage 2

Year 4