The Three R’s of Mathematical Practice #8 Kevin McLeod Connie Laughlin Hank Kepner Beth Schefelker Mary Mooney Math Teacher Leader Meeting, March The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

Learning Intention We are learning to deepen our understanding of “Look for and Express Regularity in Repeated Reasoning” To understand CCSS Math Practice #8 Possible answers: recursion, multiplying by 5, any number to a power, divisibility rules, looking for factors, connections between number and algebra, number of factors a factor has, which fractions terminate, The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

Launch Think of a fraction and write it on the post-it note. How could you find an equivalent decimal to the fraction you chose? Share some similarities and differences of your fractions. Turn and talk To capture the learner’s attention To activate prior knowledge To stimulate, not stymie, thinking Collect some fractions from group members The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

Looking at a Content Standard Read 8.NS.1 Highlight some phrases that connect to the launch. How did your table discussion help you understand this content standard?

Grade 8 The Number System Know that there are numbers that are not rational and approximate them by rational numbers. 8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert to decimal expansion which repeats eventually into a rational number.

Success Criteria We will be successful when we can explain a relationship of a repeating decimal to the denominator of the corresponding fraction. The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

Your table will be exploring a fraction. Explore What is 1/7 as a decimal? Your table will be exploring a fraction. Prepare a poster that shows the process used to change your fraction into a decimal. . Walk around and look for when people decide to stop dividing. Do division, make note of remainder, circle/underline, lead them down the path, but not too far…. Tables have 2/7. 3/7. 4/7. 5/7. 6/7, 8/7 Surface how many possible digits in the quotient, in the remainders?

Let’s Summarize What We See… Fraction Decimal 1/7 0.1428571428… 2/7 0.28571428571… 3/7 0.42857142857… 4/7 0.57142857142… 5/7 0.71428571428… 6/7 0.85714285714… Chart conclusions that surface from whole group Highlight that summary occurred halfway through a lesson

Have we met the content standard? Reread the Content Standard What have we shown? How have we shown it? Really? “show that the decimal expansion repeats eventually” that Revisit content standard “show that” means one thing to a student, another to a mathematician. Looking at the posters How do you know that the decimal will be .142857142857890 When mathematicians say “show that”, they are really saying “show why”

Standard for Math Practice #8 Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal.

Dipping in on table conversations What were some questions came up at your table as you worked? What questions might your students have as they engage in this task? Listen for conjectures from participants when engaged in the 1/7th task. Have participants write their questions down

Apply For a given fraction, how can you tell the maximum length of the repeating part of the decimal? Try 11ths or 13ths.

Standard for Math Practice #8 Look for and Express Regularity in Repeated Reasoning In what ways can you connect the tasks today to the title of the Standard?

Your feedback please…. Thinking about the opportunities you have to work with teachers in the classroom, as well as outside the classroom, in what ways have you engaged teachers in understanding the Standards for Math Practice?