Dear Parents and Caregivers, Thank you for the support you give to your child’s learning. We would like to share some information to help you better understand Arizona’s College and Career Ready Standards. This is one in our of letters intended to help you understand the work your child brings home. We will highlight some new language and strategies we will use to build understanding, help children make sense of numbers, and know the common methods we learned in school. This letter addresses dividing unit by whole numbers in fifth grade. End-of-year goals Students use the meaning of fractions, of and , and the relationship between multiplication and division to understand and explain why the procedures for dividing unit fractions and whole numbers makes sense. Students will apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. They will use models and equations. Division of a by a fraction is not a requirement at this grade level. Fraction vocabulary Numerator • Numerator: the number of parts of the whole being considered • Denominator: the number of equal parts created from the whole Denominator

• Equivalent fractions: two fractions that name the same amount • Unit fraction: a fraction with the numerator of 1 • Factor: an that divides evenly into another (2 • 6 = 12, 12 ÷ 2 = 6; 2 and 6 are factors of 12)

• Product: the solution to a multiplication problem • Quotient: the solution to a division problem dividend • Divisor: the quantity by which another quantity is to be divided • Dividend: a quantity to be divided

Developing the concept of dividing unit fractions Students will solve different types of division problems. In some cases, the student will know the number of groups and need to find how many are in each group.

• Four students sitting at a table were given of a pan of brownies to share. How much of a pan will each student get if they share the pan of brownies equally?

The model shows the pan divided into 4 equal shares with each share equaling of the pan.

Mesa Public Schools/Grade5/dividing unit fractions/2013 Authorization to reprint or disseminate must be granted by Mesa Public Schools (February-2014).

Another type of problem is when the number in each group is known, but the number of groups is not known.

• Angelo has 4 lbs of peanuts. He wants to give each of his friends lb. How many friends can receive lb. of peanuts? A diagram for 4 ÷ is shown below. Students explain that since there are five fifths in one whole pound, there

must be 20 fifths in 4 pounds. Therefore, Angelo could give pound to 20 friends.

1 lb. of peanuts

Students will learn to solve unit fraction division problems using equations. • How much rice will each person get if 3 people share pound of rice equally?

A student can think of as equivalent to . divided into 3 equal groups is in each group.

How to help at home

● Create real-world examples with your child. For example, how much chocolate will each person get if 3 people

share lb. of chocolate equally? How many cup servings are there in 2 cups of raisins?

● Check for reasonableness of answers by listening to how your child came to the solution.

● Watch these videos from LearnZillion about dividing unit fractions by whole numbers and whole numbers divided by unit fractions. http://learnzillion.com/lessonsets/737-divide-whole-numbers-by-unit-fractions-and-unit-fractions-by-whole-numbers

● Remember, making mistakes is part of learning.

Mesa Public Schools/Grade5/dividing unit fractions/2013 Authorization to reprint or disseminate must be granted by Mesa Public Schools (February-2014).