Oklahoma Academic Standards Mathematics: 6.N.4.1, 6.N.4.2, Virginia - Mathematics Standards of Learning (2009): 6.4, 6.6a, 6.6b

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1 1 U n t er r ich t splan Divid ing a Whole Number by a Fraction Altersgruppe: Grade 6 Texas - TEKS: G5.3.N O.L Mathematics Florida Standards (MAFS): 6.N S.1.1 Fairfax County Public Schools Program of Studies: 6.4.a.2, 6.6.a.1, 6.6.b.3 Oklahoma Academic Standards Mathematics: 6.N.4.1, 6.N.4.2, 6.N.4.3, 6.N.4.4 Virginia - Mathematics Standards of Learning (2009): 6.4, 6.6a, 6.6b Minnesota: , Alaska: 5.N F.7, 6.N S.2 Nebraska Mathematics Standards: M A a South Carolina: 6.N S.1 Indiana: 5.C.7, 6.C.4 Georgia Standards of Excellence: M GSE 6.N S.1 Virginia - Mathematics Standards of Learning (2016): 6.5.a Online-Ressourcen: Wat e r Do wn Opening Teacher present s Students pract ice Math Pract ice Worksheet Closing M at h Obj ect ives E xpe ri e nc e a visual representation of quotative division

2 2 P rac t i c e using repeated subtraction to solve division problems Learn to divide whole numbers by fractions De vel o p a conceptual understanding of division by fractions Ope ni ng 6 Display the following problem: Ask the students to write a word problem in their notebook that the expression could be used to solve. When the students have finished writing, share. Ask several students to read their problems. The problems will fall into two categories: quotative division, where the student asks how many groups of 2 exist in 8, and partitive division, where the student asks how many items belong in each of 2 equal groups when there are 8 items. An example of quotative division is: There are 8 cookies. If a serving is 2 cookies, how many servings are there? An example of partitive division is, There are 8 cookies. If we place them in 2 bags, how many cookies belong in each bag? Say: In today s episode, we will be asking how many small containers of water are needed to fill a larger container of water. T e ac he r prese nt s M at h game : Wat e r Do wn - Quo t at i ve Di vi si o n: F rac t i o ns 12 Present Matific s episode Wat e r Do wn - Quo t at i ve Di vi si o n: F rac t i o ns to the class, using the projector. The goal of the episode is to explore division of a whole number by a fraction

3 3 by detering how many smaller containers of water are needed to fill a larger container. Example : Say: Please read the instructions. Students can read the instructions. Ask: What can we do with the containers to answer the question? The answer depends on whether the episode asks how many smaller containers are needed to fill the larger container or how many smaller containers can be filled from the larger container. Here are answers to each: 1. Pour the water from the smaller container into the larger container. Fill the smaller container again with water from the tap. Repeat until the larger container is full. Count the number of times the smaller container was poured into the larger. 2. Pour water from the larger container into the smaller container. Empty the smaller container into the flowers. Repeat until the larger container is empty. Count the number of times the larger container was emptied into the smaller. Move the containers as the students suggest, counting as you do. Enter the answer by clicking on the. If the answer is correct, the episode will present an equation related to the problem. If the answer is incorrect, the question will wiggle.

4 4 Click on the to continue. The episode will present a total of five questions. The third and fourth problems will present division problems without referencing the containers, although the containers are still available to use. The fifth problem will ask for the volume of the smaller cup. St ude nt s prac t i c e M at h game : Wat e r Do wn - Quo t at i ve Di vi si o n: F rac t i o ns 14 Have the students play Wat e r Do wn - Quo t at i ve Di vi si o n: F rac t i o ns and Wat e r Do wn - Quo t at i ve Di vi si o n: P uzzl e s. on their personal devices. Circulate, answering questions as necessary. M at h P rac t i c e : Di vi di ng a Who l e N umbe r by a F rac t i o n Wo rkshe e t 12 Display the following problem: Have the students work in pairs. Ask them to find the quotient and draw a picture with containers to illustrate the problem and answer. Finally, ask them to write a few sentences explaining what the answer means. Circulate, answering questions as necessary. When the students are done, collect work, to display later. A possible solution: L container 1 L container

5 5 The quotient is. This means that we need of the smaller containers to fill the larger container. When we pour of a liter of water into the 1 L container, there is room left. When we again fill the L container, we cannot fit all of the water into the larger container. Only of a liter fits, which is of the smaller container. So we can fit water from 1 small container and of a small container into the larger container.

6 6 Cl o si ng 3 Display the following problem: Ask: What is the quotient? How do you know? The quotient is 16. We can pour 8 containers of size L into a 1 L container. So we can pour twice that into a 2 L container. Say: When we divide a whole number by a proper fraction, the quotient is always larger than the dividend. Why? A proper fraction is smaller than 1. So when we ask how many times it fits inside 1, the answer has to be greater than 1. So if the fraction fits inside 1 more than once, it will fit inside 2 more than twice, and fit inside 3 more than three times, etc.