Rename improper fractions as mixed numbers and position improper fractions on a number line.

Number Framework Stage 7

Students often believe fractions must be less than 1 because they are thinking about a fraction of 1 whole. A more general view of fractions is needed. This activity revisitsthis important idea.

#### Using Materials

Problem: “Kate’s Kitchen sells pizza pieces. Each pizza is cut into 4 equal pieces. At the end of the day, the computer shows Kate has sold 13 pieces of pizza. How much pizza has she sold?”

*(Answer: Modelling pizza with 13 quarters, and forming them into 3 wholes and 1 **quarter shows 13/4 = 3 1/4.)*

Examples: Using word stories convert these fractions to mixed fractions: 15/4, 11/3, 12/4, 17/6, 19/3, 24/4...

Problem: “Imagine 19 pieces of pizza where each piece is a fifth of a pizza. How many pizzas is this?”

Write 19/5 = on the board. Have the students discuss how this is 3 4/5.

Examples: Using word stories, convert these fractions to mixed fractions. Imagine pieces of pizza: 15/7, 11/6, 30/6, 27/10, 19/4, 24/7...

#### Using Number Properties

Problem: “At a party, Jules gives his guests 1 tenth of a cake each to eat. He has 112 guests. How many cakes are eaten?” *(Answer: 11 2/10.)*

Examples: Using word stories convert these fractions to mixed fractions: 101/10, 31/3, 99/11, 52/5, 41/8, 103/20...

Problem: “Moana has 10 1/6 pizzas in her fridge for a party. She plans to give 1/6 of a pizza to each guest. How many guests will get a piece of pizza?”

Discuss why the answer is 10 x 6 + 1 = 61, and write 10 1/6 = 61/6 on the board.

Examples: Convert these fractions to common fractions: 3 1/10, 7 2/3, 1 23/24, 12 2/5, 6 7/8, 3 5/12...

#### Understanding Number Properties

Describe how to convert 120 4/5 to a common fraction.*(Answer: Multiply the whole number (120) by the denominator (5) and add to the **numerator (4), the answer 604 is the numerator, 5 is the denominator. So 120 4/5 = 604/5.)*

#### Understanding Number Properties

*Describe how to convert 209/5 into a mixed fraction.
(Answer: Divide the numerator (209) by the denominator (5), this gives the whole number part of the mixed fraction, 41. Put the remainder as the numerator over the denominator, 4/5 . So = 209/5 = 41 4/5.)*