CCSS-M: Fractions Part 1

Teaching for Understanding We Are Learning To: Examine fractions as numbers using models Deepen understanding of partitioning Understand and use unit fraction reasoning Analyze fraction standards from the CCSS in grades 1, 2, and 3. 2.5 min

Success Criteria We know we are successful when we can… Clearly explain the mathematical content in 1G3, 2G3, and 3NF1 and be able to provide examples of the mathematics. 2.5 min.

10 sec.

Launch: Fractions as Numbers 3 4 What are ways we want students to “see” and “think about” fractions? Ask teachers to think about ¾ before the ideas of equivalency, comparing, ordering or operating. Table discussion 5 minutes Whole group 5 minutes Chart Ideas that are generated: set model, area model, number line, use of unit fractions, equal size pieces, equal amount pieces, ¼ + ¼ Write and draw ways students should see and think about this number. * Students often see fractions as two whole numbers Teach: -

CCSS 1G3 and 2G3 What does 1G3 mean? Individually do numbers 1 and 2. Read the standard. Highlight key words and key phrases from the standard. Provide examples for the highlighted ideas. Table share Repeat this 3 step process for 2G3 15 minutes a timed activity. Provide a copy of the designated standards in a grid where the second column is for notes and examples. 3 step process: Individually do numbers 1 and 2. 1) read the standard. Highlight key words and key phrases from the standard. Provide examples for the highlighted ideas. 3) Table share

Slate Work Take a slate and divide it in half On side show your understanding of 1G3 and on the other side show your understanding of 2 G3 Use the language of the two standards to explain your picture to your partner.

Pulling Ideas Together What representations should we add based on the analysis of standards 1G3 and 2G3? 2) Summary : What ‘big ideas’ about these standards would you share with your primary teachers? Whole group to add to chart – 5 min. Summary statement: Table group 5 min. Summary statement should be a concise and written on the back of their standard grid form.

Examining Partitioning ....“early experiences with physically partitioning objects or sets of objects may be as important to a child’s development of fraction concepts as counting is to their development of whole number concepts” (Behr and Post, 1992) Partitioning leads to fraction concepts such as: identifying fair shares fractional parts of an object fractional parts of a set comparing and ordering locating fractions on a number line density of rational numbers equivalency of fractions operating with fractions measuring helps when students have difficulty recognizing fractional parts as equal sizes if the pieces are not congruent.

Stages of Partitioning Read pgs. 71 – 75 (through stages of partitioning) Highlight key phrases from the reading * Star the important ideas ? Question mark the confusing thoughts Table group discussion summarizing and clarifying thoughts Work through problem number 1 on pages 77 & 78 Problem number 1 highlights the inaprorpriate use of whole number reasoning – use the magnitude of the denominator to locate the fractions on a number line.

Fraction Models: Area, Set, and Number Line Features of Fraction Models How the whole is defined How “equal parts” are defined and What the fraction indicates Participants refer to the chart on pg. 9 in their book after a short partner discussion. Notes: three pans of brownies in which the wholes are physically separate number line from 0 to 3 in which the wholes are not physically separate, but continuous

Slate Work Take a slate and divide it in thirds On each 1/3 draw a model; a area model, a set model, and a number line. Discuss the features of each model.

Features of Models What is the whole? How are equal parts defined? What does the fraction indicate? Area Model The whole is determined by the area of a defined region Equal area The part covered of whole unit area Set Model The whole is determined by definition (of what is in the set) Equal number of objects The count of objects in the subset of the defined set of objects. Number Line Unit of distance or length (continuous) Equal distance The location of a point in relation to the distance from zero with regard to the defined unit. Whole group discussion: What ideas make more sense to you now?

Explore Fractions Strips Why is it important for students to fold their own fraction strips? How does the “cognitive demand” change when you provide prepared fraction strips? Should fraction strips be labeled with numerals? 10 min. Participants put their fraction strips in front of them on the table and table group discussion on the three questions. Revisit labeling fraction strips with numerals after several activities.

Focusing on Unit Fractions Fold each fraction strip so you can only see one “unit” of each strip. Arrange these unit fractions from largest to smallest. What conjectures can you make about unit fractions? 5 to 10 min. This is definitely an area of misconceptions. Inappropriate use of whole number reasoning. 5 is bigger than 4 but 1/5 is smaller than ¼.

Fractions Composed of Unit Fractions Fold your fraction strip to show ¾ How do you see this fraction as ‘unit fractions’? 5 min.

Looking at a Whole Arrange the open fraction strips in front of you. Look at the thirds strip. How do you see the number 1 on this strip using unit fractions? In pairs, practice stating the relationship between the whole and the number of unit fractions in that whole (e.g., 3/3 is three parts of size 1/3). 5 min

CCSS 3NF 1 Understand a fraction1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. How do you make sense of the language in this standard connected to the previous activity? 10 min.

Extension of Unit Fraction Reasoning Jason hiked 3/7 of the way around Devil’s Lake. Jenny hiked 3/5 of the way around the lake. Who hiked the farthest? Use fraction strips and reasoning to explain your answer to this question.

Extension 2 Jim and Sarah each have a garden. The gardens are the same size. 5/6 of Jim’s garden is planted with corn. 7/8 of Sarah’s garden is planted with corn. Who has planted more corn in their garden? Use fraction strips and reasoning to explain your answer to this question.

Slate Work After your group discusses the answer to the problem, write on your slate the reasoning that you used to explain your answer. Be sure your reasoning is connected to unit fractions and fraction strips.

Extension 3 Suzette ate 1 ½ cupcakes. Marybeth ate 9/8 cupcakes. Who ate more? Use diagrams and words to explain your answer. What are the student misconceptions? Use slates.

Standards for Mathematical Practice with mc cullum graphic. Discussions about which practices we saw/did today. How does clustering the practices help you with this discussion? 1,2,4,5 E Be explicit. http://commoncoretools.files.wordpress.com/2011/03/practices.pdf

Let’s Rethink the Day We know we are successful when we can… Clearly explain the mathematical content in 1G3, 2G3, and 3NF1 and be able to provide examples of the mathematics. Depending on time either the participants engage in a discussion or there is a whole group discussion of big ideas from the day.