Welcome Back! 3rd Grade Planning December 9, 2014 8:00 – 10:45 am

Survey Results

Survey Results: Current Curriculum

Guiding Questions for Today Standards: What are the 3rd grade CC content standards for measurement & data and for fractions? Curriculum: What experiences does Math Expressions offer in Unit 3? What experiences are coming up in Unit 7, Explore Fractions? What experiences did the DILs provide in the PUSD Unit 3? How might we integrate the experiences in the two resources? Instruction: How much instruction should we provide about fractions now? What other experiences should we add in?

3rd Grade T2 Data The sharing cookies problem – The Doorbell Rang

T2 Linear Measurement and Fractional Line Plots Fraction strips and number lines.

T2 Time, Mass, Volume Number Lines for time

Area and Perimeter Part of T1 Standards – Not in Unit 3.

3rd Grade CC Fractions (T3) Overview What is a fraction? How can I make fractions from unit fractions? How can I compare fractions? How can I find equivalent fractions? How is a fraction strip model similar and/or different from a number line model? All notes and examples in this section came from the California CC Math Framework

Using Fraction Strips to Understand the Role of Unit Fractions in All Fractions

Representing Fractions on the Number Line

Fractions Greater than One

Connecting Fraction Strips and the Number Line

Equivalent Fractions with Fraction Strips

Equivalent Fractions on the Number Line

Math Expressions Brief Self-Tour Give yourself a brief tour of chapter 3. TE pages 293S – 293JJ What do you notice? Give yourself a brief tour of chapter 7. TE pages 743Q – 743FF What parts of this chapter might be relevant now for success with fractional measurements? Fractions are an major standard for 3rd grade. What are the SBAC implications if this is our last chapter? Are there any pacing adjustments we can make?

A Perspective on Textbooks: An argument for professional decision making (Phil Daro) Each lesson is written for 5 different teacher “types” or perspectives. A lesson was never intended to be taught in its entirety. Publishers anticipate you will use what fits into your perspective. You know more than the publisher. Trust yourself to make informed curriculum decisions.

PUSD Unit of Study ME Chapter 3, Measurement, Time, and Graphs Pathway: My Connect Math Central Units of Study 3rd Grade Unit 3 …Or in our GoogleDoc so you can edit. Have everyone access the unit. Also, make sure at least half the participants can access the google doc with the Word version of the unit.

With a Partner . . . Explore some of the measurement activities offered in the PUSD unit. What standard is addressed each experience? What mathematical practices are the students engaged in? How might it be integrated into your work with Math Expressions? Add any useful notes to the unit.

A Fraction/Measurement Foundation Sequence Make a Fraction Kit (halves, fourths, eighths) Play Cover Up and Uncover Transition to the Number Line Transition to Standard Measurement (Constructing a Ruler) Fraction Kit: Guide the students as they each make a fraction kit, asking questions as they fold and cut: “If I fold this ‘whole’ fraction strip in half, when I open it up, how many equal pieces will I have?” “Let’s label each piece. Each piece represents one out of two equal pieces, how do I write that? What does the 1 mean? What does the 2 mean? (write ½) What is the top number called? What is the bottom number called?” “If I fold this whole fraction strip in half and then fold it in half again, when I open it up, how many equal pieces will I have?” “If I fold this whole fraction strip in half and then fold it in half again and then fold it in half again, when I open it up, how many equal pieces will I have?” Have students record the relationships that they notice. You can model a few. “I see that 2/4 = ½.” OR ½ > ¼ OR ¼ + ¾ = 4/4 = 1 Cover Up and Uncover: Play Cover Up and Uncover (the game calls for halves, fourths, eights, and sixteenths but we only made kits up to eighths so you will need modified dice, spinners, cards . . .. A die would have its sides labeled with the fractions: ½, ¼, ¼, 1/8, 1/8, 1/8. Transition to Fractions as measures of length (construct a number line): Transition to fractions as length on a Number Line: If I drew a line the same length as my whole, and instead of looking at the size of the piece, I looked at the length of it, where would I write 0? Where would I write 1? Where would I write 0/2,?½?, 2/2? Why? (show with fraction strips and then remove and mark the number line with tic marks). Where would I write 0/4? ¼? Why? (always help them visualize with the fraction strips). Where would 2/4 go? Why? Where would ¾ go? Why? Where would 4/4 go? Why? What would come next? Have students construct a number line based on the fraction strip lengths. You can have them go around the room and find things that are about 1 fraction strip long, ½ fraction strip long, etc. . . . Standard versus Nonstandard Units of Measure: This might be a nice time to build in a lesson helping them see the importance of standard units. You could fill in the lesson of Foot Length Rulers and How Big is a Foot. Construct a Ruler and Measure– fractions of a foot: Change the Whole: Give students a blank strip of paper (make sure it is 12 inches long but don’t tell them). Have them mark 0/2, ½, 2/2 and 0/4, ¼, 2/4, ¾, 4/4. Tell them this ruler is 1 foot in length. Have them measure different objects using halves and fourths of a foot. Construct Ruler and Measure – inches and fractions of an inch: Give another blank strip of paper (12 inches in length). Give students color tiles. Let them know the color tiles are 1 inch each. “How many color tiles/inches long is a foot?” Have students iterate the color tiles and draw tic marks at each inch. Have them write in the inches: 1, 2, 3 . . . Ask them, where is ½ foot? (connect to their previous ruler.” “This time, we are going to mark the fractions of each inch . . . Between 0 and 1 inch, where would ½ go? Where would ¼ go? What else could you label?” Demo measuring to nearest quarter inch. Have students practice measuring objects around the room and recording their measurements. Constructing a line plot: Have partners measure their pencils to the nearest ¼ inch. Co-construct an axis for the line plot and discuss how to mark it with a ¼ inch scale. Have students report their data while you demonstrate marking it on the plot (dots or x’s are typical). Ask students to make statements from looking at the line plot. You can ask them standards-based questions. How many students have a pencil that is 5 ½ inches long? What is the most common length in our class? How many students had a pencil that was at least 6 inches long? How many pencils were less than 5 ¼ inches long? How many more students have a pencil that ___ inches long versus ____ inches long? Etc.

Additional Resources Fractions: http://www.k-5mathteachingresources.com/3rd-grade-number-activities.html Measurement: http://www.k-5mathteachingresources.com/3rd-grade-measurement-and-data.html