Copy this square exactly and shade in a quarter in as many different ways as you can. You have 5 minutes

What does equivalent mean? LO: To change between equivalent fractions including improper and mixed numbers (5) To order fractions by using equivalence (6) What does equivalent mean?

3 6 18 = = 4 8 24 Equivalent fractions Look at this diagram: ×2 ×3 ×2 Ask pupils what proportion of the diagram is shaded (3/4). Look what happens if we cut each quarter into two equal parts. Click to divide. We now have 1/8s. Exactly the same amount is shaded, but you can see how we can call this amount 6/8? What have we done by cutting each quarter into two equal parts? Explain that we have multiplied the number of shaded sections by two (we had three shaded sections; now we have six) and we have multiplied the number of equal parts by two (we had four; now we have eight). Click to reveal the arrows showing the numerator and the denominator being multiplied by 2. We’ve multiplied the numerator by 2 and the denominator by 2. The numbers have changed but exactly the same proportion of the circle has been shaded. 3/4 and 6/8 are equivalent fractions. We could divide each of these eights into three equal parts. Look what happens. Click to reveal. Now, how many equal parts are there altogether? (3 x 8, 24) How many of those equal parts are shaded? (3 x 6, 18) So we now have 18 out of 24 parts shaded. Click to reveal this fraction. Explain that we have multiplied both the numerator and the denominator by three. The numbers have changed but exactly the same proportion of the circle has been shaded. What would we multiply the numerator and the denominator of 3/4 by to get 18/24? (6) You can se that each quarter of our original diagram has been divided into six equal parts. 3/4, 6/8 and 18/24 are equivalent fractions. Can you think of any other fractions that are equal to ¾? In how many different ways could we write ¾? (Infinitely many!) 3 6 18 = = 4 8 24 ×2 ×3

2 6 24 = = 3 9 36 Equivalent fractions Look at this diagram: ×3 ×4 ×3 Explain this set of equivalent fractions as in the previous slide. 2 6 24 = = 3 9 36 ×3 ×4

18 6 3 = = 30 10 5 Equivalent fractions Look at this diagram: ÷3 ÷2 ÷3 Ask pupils what proportion of the diagram is shaded. (18/30) We could simplify this diagram by removing these horizontal lines. Click to remove some of the horizontal divisions. We now have ten equal parts. Exactly the same amount is shaded, but you can see how we can call this amount 6/10. By removing those horizontal lines we have made every 3/30 into 1/10. Explain that we have divided the number of shaded sections by 3 (we had 18 shaded sections; now we have 6) and we have divided the number of equal parts by 3 (we had 30; now we have 10). Click to reveal the arrows showing the numerator and the denominator being divided by 3. 18/30 and 6/10 are equivalent fractions. Tell pupils that by dividing the numerator and the denominator by the same number, we have simplified the fraction. It is simpler because the numbers are smaller. Can we simplify this fraction any further? Yes, 6 and 10 are both even numbers, so we could divide the numerator and the denominator by 2. Remember, if we divide the numerator and the denominator by the same number the numbers that make up the fraction change but the fraction itself has exactly the same value. Click to show the numerator and the denominator being divided by 2. 6/10 is equivalent to 3/5. We can see this in the diagram by grouping each 2 tenths into one fifth. Click to reveal. Can we simplify 3/5 any further?” No, 3 and 5 have no common factors, there is no number which divides into both 3 and 5.” We have expressed the fraction 18/30 in its lowest terms. This is also called cancelling the fraction down. How could we have cancelled 18/30 to its simplest form in one step? Establish that we could have divided the numerator and the denominator by 6. We call 6 the highest common factor of 18 and 30. 18 6 3 = = 30 10 5 ÷3 ÷2

Equivalent Fractions * Extension * Write as many fractions as you can that are equivalent to 𝟑 𝟓

LO: To change between equivalent fractions including improper and mixed numbers (5) To order fractions by using equivalence (6)

Step 1: Find the lowest common multiple of 8 and 12. Which is bigger or ? 3 8 5 12 Another way to compare two fractions is to convert them to equivalent fractions. Step 1: Find the lowest common multiple of 8 and 12. The lowest common multiple of 8 and 12 is 24. Now, write and as equivalent fractions over 24. 3 8 5 12 Tell pupils that another way to compare two fractions is to convert them into equivalent fractions with a common denominator. Talk through the example on the board. Tell pupils that the quickest way to find the lowest common multiple of two numbers is to choose the larger number and to go through multiples of this number until we find a multiple which is also a multiple of the smaller number. This method also works for a group of numbers. ×3 ×2 3 8 = 24 9 5 12 = 24 10 3 8 5 12 < and so, ×3 ×2

Ask pupils to order the fractions on the board using an appropriate method.

Ordering Fractions For each question, put the fractions in order: 1 2 3 4 1 4 3 8 7 8 Clue: make them all into eighths 1 6 3 9 1 3 4 18 10 18 1 5 3 10 11 20 3 5 7 10

LO: To change between equivalent fractions including improper and mixed numbers (5) To order fractions by using equivalence (6) Ask pupils in turn to choose a fraction and justify where it goes by dividing the numerator and the denominator by the same number. For fraction diagrams pupils must state the fraction shaded first. Continue until all the fractions are in the correct place. Ask pupils to come up in turns and choose a fraction to drag and drop into the correct place.

A fraction that is bigger than 1 But does NOT have a denominator of 2 Show me A fraction that is bigger than 1 But does NOT have a denominator of 2 2

A fraction that is bigger than 1 But does NOT have a denominator of 3 Show me A fraction that is bigger than 1 But does NOT have a denominator of 3 3

A fraction that is bigger than 2 But does NOT have a denominator of 3 Show me A fraction that is bigger than 2 But does NOT have a denominator of 3 3

A fraction that is equivalent to 2 Show me A fraction that is equivalent to 2 3

A fraction that is equivalent to 5 Show me A fraction that is equivalent to 5 8

LO: To change between improper and mixed numbers (5)

LO: To change between improper and mixed numbers (5) STARTER - put the fractions in order: 1 6 3 9 1 3 4 6 7 9 Clue: make them all into ninths 1 6 3 4 1 8 4 24 10 24 Clue: make them all into twenty-fourths

3 LO: To change between improper and mixed numbers (5) Improper fraction – When the numerator of a fraction is larger than the denominator For example, 15 4 is an improper fraction. We can write improper fractions as mixed numbers. 15 4 Talk through the diagrammatic representation of 15/4. Every four quarters are grouped into one whole, and there are three quarters left over. can be shown as 15 4 3 4 =

LO: To change between improper and mixed numbers (5) Convert to a mixed number. 37 8 37 8 = 8 + 5 5 8 1 + = = 4 5 8 This number is the remainder. Explain that to convert an improper fraction to a mixed number we can divide the numerator by the denominator to find the value of the whole number part. Any remainder is written as a fraction. Relate fractions to division. 37/8 means 37 ÷ 8. Talk through the division of 37 by 8. Discuss the meaning of the remainder in this context. We are dividing by 8 and so the 5 represents 5/8. 37 8 = 4 4 5 8 5 37 ÷ 8 = 4 remainder 5 This is the number of times 8 divides into 37.

LO: To change between improper and mixed numbers (5) Convert these improper fractions into mixed numbers: 1a) 5/3 1b) 21/5 1c) 33/5 2a) 11/4 2b) 19/3 2c) 50/6 3a) 10/3 3b) 27/8 3c) 39/4 4b) 15/2 4c) 40/12 4a) 9/8

LO: To change between improper and mixed numbers (5) Now check your answers… 1a) 12/3 1b) 41/5 1c) 63/5 2a) 23/4 2b) 61/3 2c) 82/3 3a) 31/3 3b) 33/8 3c) 93/4 4b) 71/2 4c) 34/12 4a) 11/8

LO: To change between improper and mixed numbers (5) Convert to an improper fraction 2 7 3 2 7 3 = 2 7 1 + = 7 + 2 = 23 7 … and add this number … To do this in one step, We can explain this conversion by asking for the number of 1/7 in 3 whole ones. Explain that there are 21 sevenths in three wholes. Two more sevenths makes 23 sevenths altogether. Explain that to convert a mixed number to an improper fraction in one step we multiply the whole number part by the denominator of the fractional part and add the numerator of the fractional part (refer to the example). This gives us the numerator of the improper fraction. The denominator of the improper fraction is the same as the fractional part of the mixed number. 3 3 2 2 23 … to get the numerator. = 7 7 7 Multiply these numbers together …

LO: To change between improper and mixed numbers (5) Convert these mixed numbers into improper fractions 1a) 11/2 1b) 32/3 1c) 52/3 2a) 21/4 2b) 51/4 2c) 23/5 3a) 31/5 3b) 42/5 3c) 63/8 4b) 61/3 4c) 42/8 4a) 41/2

LO: To change between improper and mixed numbers (5) Now check your answers… 1a) 3/2 1b) 11/3 1c) 17/3 2a) 9/4 2b) 21/4 2c) 13/5 3a) 16/5 3b) 22/5 3c) 51/8 4b) 19/3 4c) 34/8 4a) 9/2

Find the missing number In this activity equivalent fractions, mixed numbers and improper fractions are generated. Ask pupils to find the value of the missing number, explaining their reasoning.

* WAGOLL * * WAGOLL * Convert mixed to improper: Convert improper to mixed: * WAGOLL *