Compare Fractions with the Same Numerator MAFS.3.NF.1.3d

Lesson Opening A B A B F C A B E D C D If you receive $1 for every time you spin the spinner and landed on the letter A, which spinner would you choose? Why? A B A B F C A B E D C D

Lesson Opening A B A B F C A B E D C D 1 2 is the largest fraction, so you have the best chance to earn the most money with the yellow spinner. Lesson Opening If you receive $1 for every time you spin the spinner and landed on the letter A, which spinner would you choose? Why? A B A B F C A B E D C D You have a 1 out of 4 chance for spinning A. We write this 1 4 . You have a 1 out of 2 chance for spinning A. We write this 1 2 . You have a 1 out of 6 chance for spinning A. We write this 1 6 .

Look at the models 𝟏 𝟒 𝟏 𝟐 𝟏 𝟔 Number of pieces referred to (or shaded in) Number of pieces referred to (or shaded in) Number of pieces referred to (or shaded in) Number of pieces in the whole Number of pieces in the whole Number of pieces in the whole

They each have 1 piece shaded in They each have 1 piece shaded in. So, all we have to compare is the SIZE of each piece. Which pie has the LARGEST pieces? The pie partitioned into halves. The denominator with the smallest number gives you the BIGGEST size pieces. 𝟏 𝟒 𝟏 𝟐 𝟏 𝟔 Number of pieces referred to (or shaded in) Number of pieces referred to (or shaded in) Number of pieces referred to (or shaded in) Number of pieces in the whole Number of pieces in the whole Number of pieces in the whole

Is this true with your fraction tiles? 𝟏 𝟏 What is your biggest fraction piece? What is your next biggest fraction piece? What is your SMALLEST fraction piece? 𝟏 𝟐 𝟏 𝟑 𝟏 𝟒 𝟏 𝟏𝟐

Is this true with your fraction tiles? 𝟏 𝟏 What is your biggest fraction piece? What is your next biggest fraction piece? What is your SMALLEST fraction piece? 𝟏 𝟐 What happens to the DENOMINATOR as your pieces get smaller? 𝟏 𝟑 𝟏 𝟒 The number in the denominator gets bigger. (because the whole is partitioned into more pieces) 𝟏 𝟏𝟐

Same Numerator = Same number of pieces being referred to So if… The fractions refer to the same whole, and The numerators are the SAME, Then, the number of pieces being compared is the same. Then, what are you comparing? Just the denominator, or, the size of each piece.

Let’s compare! Sixths are bigger than eighths, so 𝟐 𝟔 is bigger than 𝟐 𝟖 . So, Jerry ate more pie. Tom and Jerry each made pie. The pies were the same size. Tom cut his pie into 8 slices; Jerry cut his into 6 slices. They each ate 2 slices of their own pie. Who ate more? Draw a model. Write the fraction that each ate. Tom Jerry Did they eat the same NUMBER of pieces? (Are the numerators the same?) 𝟐 𝟖 𝟐 𝟔 Then compare the SIZE of the pieces. Or, compare the denominators.

The number of spaces from 0 is the same The number of spaces from 0 is the same. But the size of each space is different. All we need to compare is the size of each space (which is the denominator). You can use a NUMBER LINE to compare fractions with the same numerator, too. Compare: 2 3 and 2 8 1 3 2 3 1 1 8 2 8 3 8 4 8 5 8 6 8 7 8 1

> < < < < > 3 4 3 8 5 6 5 2 2 5 2 3 5 8 5 4 1 3 1 2 Your Turn 3 4 3 8 5 6 5 2 2 5 2 3 > 5 8 5 4 1 3 1 2 7 8 4 8 < < < < >

Your Turn

The number of pieces being referred to is the same. Lesson Closing If the wholes are the same size and the numerators are the same, what does that mean? What is a rule for comparing fractions when the numerator is the same? The number of pieces being referred to is the same. If the number of pieces are the same size (according to the numerator) then compare the SIZE of the pieces (the denominator).

3 6 3 8 3 2 3 4 Exit Ticket GRIDDED RESPONSE GRIDDED RESPONSE 1. Which is the smallest fraction? 2. Write a fraction with the SAME numerator that is larger than 3 4 . 3 6 3 8 3 2 3 4 GRIDDED RESPONSE