James and Mary are making cookies James and Mary are making cookies.  James has 1 2 cup of sugar and Mary has 1 3 cup.  About how much sugar do they have?  Is 1 3 closer to 1 whole or one half? If we add 1 3 and 1 2 together, will my answer be closer to 1 whole or 2?

LearnZillion Notes: --This is our lesson objective. Keep it as short and student-friendly as possible. Put what they will learn in green and then how they’ll learn it in blue. For example, “In this lesson you will learn how to compare fractions with different denominators by using a number line.”

1 4 2 4 3 4 4 4 One dollar = four quarters. Half a dollar = two quarters Our number line is divided into fourths for the four parts of a dollar or four quarters that make up a dollar. The dollar idea gives us a great every day way to think about benchmark fractions such as ¼, ½, and ¾. We will use this idea in this lesson to work with benchmark fractions as a way to estimate for the reasonableness of our answers to story problem fractions.

1 4 > 1 2 > 1 4 < 1 2 Thinking about fractions, some students may think that the larger denominator automatically means the larger fraction even if the numerator is small. 1 4 is larger than 1 2 because the denominator 4 is larger than the denominator 2. So, 1 4 is closer to 1 whole than 1 2 . When we look at the fraction bar, does 1 out of 4 look like more than 1 out of 2? No. We know that this statement is false and that the denominator alone does not determine the value of the fraction.

Fractions close to 1 2 have numerators that are about (one half of) the denominator. Tari has 3 8 of a bag of puppy food for her new puppy. Her mom said to add it to the grocery list when she had about 1 2 of a bag. Does Tari need to add puppy food to the list? Does Tari need to add puppy food to the list? Yes. Mom said about a half of a bag. Tari has 3/8 of a bag left. Fractions that have a numerator which is ½ of the denominator are 1/2 We can think that 4 out of 8 would be half and this is 3 out of 8, so we have less than 1/2

Mikki is bringing cookies to Tari’s house for a sleepover and to meet Tari’s new puppy. Mikki has 5 8 of a bag of chocolate chip cookies and 1 4 a bag of oatmeal cookies. Does Mikki have a full bag of cookies to bring to Tari’s house? Does Mikki have a full bag of cookies? 5/8 – Think – 5 out of 8 is very close to 4 out of 8 which would be one half. ¼ - Think – 1 out of 4 is very little, only one quarter of a dollar, and not close to ½. ½ plus less than one half would be close to one whole. Mikki would have close to a full bag of cookies. Let’s see this on a number line. If we added the ¼ shaded in blue to the 5/8 number line, it shows that we would have 7/8 of a bag which is almost one full bag!

Sarah has 7 8 of the money she needs for a movie ticket Sarah has 7 8 of the money she needs for a movie ticket. Her brother Lee has 1 3 4 of the money he needs for a movie ticket. If they combine their money, will they have enough for two tickets? 1 7 out of 8 means that almost all of the number line would be shaded in, all but one part. 1 and 3 out of four means that all of number line and almost all of the second model would be shaded in, all but one part. We can estimate that they would have almost enough for two whole tickets.

Anthony has sold 1 1 5 of a box full of Boy Scout cookies for his troop. His sister Anna has sold 9 10 of a box full of Girl Scout cookies. Who has sold more cookies? 1 1 1 We know that Anthony has sold 1 whole and 1 out of 5 boxes of cookies. 1 out of 5 is smaller than 1 out of 4 and we know that 1 out of 4 is the same a one quarter of a dollar or 25 cents. So Anthony has sold one and very little of another. Let’s see this on a number line. We know that Anna has sold 9 out of 10 boxes of cookies. That would mean 9 out of 10 shaded on a model or number line leaving only one piece not shaded. So Anna has sold almost one whole. Since Anthony has sold one whole and a small part of another whole, he has sold more cookies than his sister Anna.

Using the benchmark fractions 1 4 , 1 2 , and 3 4 , model these on number lines, model two fractions that are equivalent using additional number lines. Create a story problem to go with your equivalent fractions.

Describe three fractions that are: Close to one-fourth Close to one-half Close to three-fourths Close to one whole. For each example, explain your reasoning using full sentences.

Tari has 11 13 of the rocks she needs for her fish tank Tari has 11 13 of the rocks she needs for her fish tank. Is 11 13 closer to one-half or one-whole? Mikki needs 1 2 of her room painted light pink. She has 12 24 completed so far. Is she finished?