Number String Mini-Lessons

1. Number String Mini-Lessons MET21 Professional Learning August 8, 2011

2. Objectives • Summarize the pedagogy in mini-lessons. • Practice drawing representations of student thinking. • Experience the role of learner during a mini-lessons.

3. “Look to the numbers first. Use the strategy that the numbers call out to you.” - Ann Dowker

4. Number Talks – New Dimensions • Carefully crafted strings of numbers • Visual representations of student thinking • Pair Talk & Questioning strategies used to clarify and reinforce thinking. • Transition Number Talk Strategies from “Mental to Pencil” (mental during number talk and pencil when it serves as an efficient strategy for everyday use).

5. Visual Models • Addition/Subtraction • Short lines for break apart (distributive property) • Open Number Line for all others • Money Model for landmark number fluency • Multiplication/Division • Open Array (Area Model) • Open Number Line for skip counting, removing or adding a group • Ratio Table for ratio and proportional reasoning

6. Visual Representation • Teachers represent student thinking on a visual model. • That visual model of their thinking becomes a tool for thinking.

7. Learning Rotations Each learning community member will participate in 3 number string mini-lessons from different perspectives: • Participate in number string (number talk) • Practice sketching the visual representations • Study the pedagogy and take notes

8. Learning Rotations

9. The Value of Number Strings Mini-lessons • The strings are tightly structured computation problems designed to steer children toward developing a particular strategy or strategies. • The strings have developmental progression. • Calculating with number sense means having many strategies at your disposal so that children will look at the numbers first before choosing a strategy.

10. How To • More guided and explicit than investigations • Designed to be used at the start of math workshop • 15 minute mini-lessons • Use the “thumb to chest” response (GBMP) • Whole class in meeting area; cluster students for use of pair talk. • Suggested directions: Examine the numbers in the problem and think about clever, efficient ways to reach a solution.

11. Why Have Multiple Strategies • Research shows 96% of the time mathematicians do not use standard algorithms. They look at the numbers first to select the most efficient strategies. • Provide good number sense for real life applications such as: evaluating advertising claims, estimating quantities, judging reasonableness, adding up restaurant checks, determining equal shares, interpreting data and statistics, etc.

12. Standard Algorithms • “Depending on the numbers, the algorithm is often slow. It only seems faster to most adults because they have always used algorithms. The procedures have become habits that require little thinking. Calculating with number sense as a mathematician means having many strategies at your disposal and looking to the numbers first before choosing a strategy.” - Catherine Fosnot

13. Reminders • Strategies used for number talks should be encouraged during paper/pencil work when the numbers call out for them to be used. • Honor student strategies. Accept alternative solutions and explore why they work. • Use models to represent student strategies, facilitate discussions, and reflect on shared strategies. • Use the pair talk if needed for clarity, reflection, to draw more students into the lesson, and/or to allow time for the strategy to sink in for some students.

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