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 be able to provide examples of the mathematics. 2.5 min.

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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 one side show your understanding of 1G3 and, on the other side, show your understanding of 2G3 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.

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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 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 third, 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?