Unpacking Operations & Algebraic Thinking Fluency with Single-Digit Addition & Subtraction Common Core Leadership for Mathematics (CCLM) University of Wisconsin-Milwaukee DeAnn Huinker & Melissa Hedges June 22, 2011 CCLM Common Core Leadership in Mathematics Project

“Fluency” in the CCSSM Revisit the discussion of fluency pp.18-19 OA Progression document (Starts with the last paragraph.) Table groups: Discuss and chart a group response to your designated prompt.

Thinking about instruction… By the end of the K-2 grade span, students have sufficient experience with addition and subtraction to know single-digit sums from memory . . . this is not a matter of instilling facts divorced from their meanings, but rather as an outcome of a multi-year process that heavily involves the interplay of practice and reasoning. p. 19 OA Progressions document How might this statement impact classroom instruction around “single-digit addition and subtraction” at all levels?

Progression toward Fluency – Subtraction Methods for solving single-digit subtraction Level 1: Direct Modeling or Taking Away Count, Count, Count Level 2: Counting on Think addition or find unknown addend Level 3: Convert to an Easier Problem Decompose a number leading to a 10

Building Understanding Through Context There were 13 cookies on the plate. Sam ate 8 of the cookies on the plate. How many cookies are on the plate now? How would a student at each level approach this problem? Note: For Level 3, be sure to examine both “Build up through ten” & “Back down through ten”

Decompose to ten: 15 – 6 Place 15 counters on the double ten frame. Completely fill one frame, place 5 on the other frame. CCSS language: “decomposing a number leading to a ten”

Decompose to ten: 15 – 6 Tell a story for 15 – 6. How can you remove 6 counters in parts by decomposing it in a way that gets you to or “leads to a ten”? CCSS language: “decomposing a number leading to a ten”

Decompose to ten: 15 – 6 Decompose 6 to remove it in parts. Remove 5 counters to get to ten.

Decompose to ten: 15 – 6 6 = 5 + 1 Remove 5 counters to get to ten. Remove 1 more.

Decompose to ten: 15 – 6 15 – 5 = 10 10 – 1 = 9 Decomposed 6 to remove 5 and then remove 1. Write an equation(s). 15 – 5 – 1 = 9 or 15 – 5 = 10 10 – 1 = 9

---------------------------- Try it: 13 – 5 16 – 7 Use ten frames and counters to reason through the “Decompose to Ten” strategy. Write an equation(s) to show the reasoning. Share and discuss in your small group. ---------------------------- Brainstorm: What other subtraction facts would lend themselves well to this strategy? Make a list of facts and try them out.