1. 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

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

3. 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?

4. 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

5. 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”

6. 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”

7. 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”

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

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

10. 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 = – 1 = 9

11. ----------------------------
Try it: – – 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.